Number Date Author Title Abstract
2721 (opens in new tab) 18.03.2018 Walloth, Mirjam Residual-type a posteriori error estimator for a quasi-static Signorini contact problem We present a new residual-type a posteriori estimator for a quasistatic Signorini problem. The theoretical results are derived for two and three-dimensional domains and the case of non-discrete gap functions is addressed. We derive global upper and lower bounds with respect to an error notion which measures the error in the displacements, the velocities and a suitable approximation of the contact forces. Further, local lower bounds for the spatial error in each time step are given. The estimator splits in temporal and spatial contributions which can be used for the adaptation of the time step as well as the mesh size. In the derivation of the estimator the local properties of the solution are exploited such that the spatial estimator has no contributions related to the non-linearities in the interior of the actual time-dependent contact zone but gives rise to an appropriate refinement of the free boundary zone.
Number Date Author Title Abstract/MSC
2720 (opens in new tab) 23.11.2017 Roch, Steffen Beyond fractality: piecewise fractal and quasifractal algebras MSC: 47N40; 54J10; 46L99
Fractality is a property of algebras of approximation sequences with several useful consequences: for example, if (An) is a sequence in a fractal algebra, then the pseudospectra of the An converge in the Hausdorff metric. The fractality of a separable algebra of approximation sequences can always be forced by a suitable restriction This observation leads to the question to describe the possible fractal restrictions of a given algebra. In this connection we define two classes of algebras beyond the class of fractal algebras (piecewise fractal and quasifractal algebras), give examples for algebras with these properties, and present some first results on the structure of quasifractal algebras (being continuous fields over the set of their fractal restrictions).
2719 (opens in new tab) 21.11.2017 Zahn, Peter Erblich endliche Mengen und die Widerspruchsfreiheit einer abgeschwächten Version von ZFC MSC: 03B10; 03C10; 03C62; 03E35; 03F50
2718 (opens in new tab) 01.12.2017 Lang, Jens
Scheichl, Robert
Adaptive Multilevel Stochastic Collocation Method for Randomized Elliptic PDEs MSC: 65C20; 65C30; 65N35; 65M75
In this paper, we propose and analyse a new adaptive multilevel stochastic collocation method for randomized elliptic PDEs. A hierarchical sequence of adaptive mesh refinements for the spatial approximation is combined with adaptive anisotropic sparse Smolyak grids in the stochastic space in such a way as to minimize computational cost. We provide a rigorous analysis for the convergence and computational complexity of the adaptive multilevel algorithm.
2717 (opens in new tab) 24.10.2017 Domschke, Pia
Hiller, Benjamin
Lang, Jens
Tischendorf, Caren
Modellierung von Gasnetzwerken: Eine Übersicht MSC: 35L; 65M; 67N
Mit dieser Übersicht wollen wir eine Zusammenstellung von unterschiedlichen Modellen zur Beschreibung des Gasflusses in Netzwerken bereitstellen, um den Einstieg in das Thema zu erleichtern. Besonderes Augenmerk wird dabei auf die der Modellierung inneliegende hierarchische Struktur und die detaillierte Beschreibung einzelner Bauteile wie Ventile und Kompressoren gelegt. Daneben finden sich ebenfalls Netzmodellklassen, die auf rein algebraische Relationen aufbauen. Am Ende geben wir einen kurzen Überblick über grundlegende numerische Verfahren und Konzepte zur Behandlung von hyperbolischen Bilanzgleichungen. Wir erheben keinen Anspruch auf Vollständigkeit und verweisen an vielen Stellen auf die bestehende Literatur. Die Idee eines Modellkataloges ist uns im Rahmen der Antragstellung zum SFB/Transregio 154 „Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken“ gekommen. Wir möchten an dieser Stelle die Förderung durch die DFG dankend erwähnen.
2716 (opens in new tab) 18.10.2017 Farwig, Reinhard
Qian, Chenyin
Asymptotic behavior for the quasi-geostrophic equations with fractional dissipation in $\mathbb{R}^2$ MSC: 37 N 10; 37 L 30
In this paper the Surface Quasi-Geostrophic Equations (QGE) with fractional dissipation in $\mathbb{R}^2$ are considered. Our aim is to study the long-time behavior of QGE in the subcritical case. To this end we investigate the global well-posedness and global attractor for QGE in $H^s(\mathbb{R}^2)$ via commutator estimates for nonlinear terms, a new iterative technique for estimates of higer order derivatives and with the help of a nonlocal damping term. Besides, by using the fractional LiebThirring inequality, estimates of the finite Hausdorff and fractal dimensions of the global attractor
are found.
2715 (opens in new tab) 07.03.2017 Roch, Steffen
Silbermann, Bernd
Toeplitz and Hankel algebras – axiomatic and asymptotic aspects MSC: 47B35; 47L80
In 1983, the authors introduced a Banach algebra of – as they called them – Toeplitz-like operators. This algebra is defined in an axiomatic way; its elements are distinguished by the existence of four related strong limits. The algebra is in the intersection of Barria and Halmos' asymptotic Toeplitz operators and of Feintuch's asymptotic Hankel operators. In the present paper, we start with repeating and extending this approach and introduce Toeplitz and Hankel operators in an abstract and axiomatic manner. In particular, we will see that our abstract Toeplitz operators can be characterized both as shift invariant operators and as compressions. Then we show that the classical Toeplitz and Hankel operators on the spaces $H^p({\mathbb T})$, $l^p({\mathbb Z}_+)$, and $L^p({\mathbb R}_+)$ are concrete realizations of our abstract Toeplitz operators. Finally we generalize some results by Didas on derivations on Toeplitz and Hankel algebras to the axiomatic context.
2714 (opens in new tab) 16.01.2017 Filonov, Nikolay
Shilkin, Timofey
On the local boundedness of weak solutions to elliptic equations with divergence-free drifts In this paper we investigate the local boundedness of weak solutions to the equation $-\Delta u + b\cdot\nabla u=0$ describing the diffusion in a stationary incompressible flow. The corresponding theory is well-known in the case of the general (not necessary divergence-free) sufficiently smooth drift (namely, for $b\in L_n$, where $n$ is the dimension of the space). Our main interest is focused on the case of $b$ with limited regularity (namely, $b\in L_2$). In this case the structure assumption $\div b=0$ turns out to be crucial. In our paper (which is partly expository) we recall some known properties of weak solution in the case of the divergence-free drifts $b\in L_2$ and also establish some new results on the local boundedness of weak solutions.
Number Date Author Title Abstract/MSC
2712 (opens in new tab) 29.11.2016 Celik, Aday
Kyed, Mads
Nonlinear Wave Equation with Damping: Periodic Forcing and Non-Resonant Solutions to the Kuznetsov Equation MSC: 35L05; 35B10; 35B34
Existence of non-resonant solutions of time-periodic type are established for the Kuznetsov equation with a periodic forcing term. The equation is considered in a three-dimensional whole-space, half-space and bounded domain, and with both non-homogeneous Dirichlet and Neumann boundary values. A method based on $L^p$ estimates of the corresponding linearization, namely the wave equation with Kelvin-Voigt damping, is employed.
2711 (opens in new tab) 31.10.2016 Eiter, Thomas
Kyed, Mads
Estimates of time-periodic fundamental solutions to the linearized Navier-Stokes equations MSC: 35Q30; 35B10; 35A08; 35E05; 76D07
Fundamental solutions to the time-periodic Stokes and Oseen linearizations of the Navier-Stokes equations in dimensions $n\geq2 are investigated.
Integrability properties and pointwise estimates are established.
2713 (opens in new tab) 20.12.2016 Walloth, Mirjam A reliable, efficient and localized error estimator for a discontinuous Galerkin method for the Signorini problem We present a new residual-type a posteriori error estimator for the discontinuous finite element solution of contact problems. The theoretical results are derived for two and three-dimensional domains and arbitrary gap functions. The estimator yields upper and lower bounds to a suitable error norm which measures the error in the displacements and in a quantity related to the contact stresses and the actual contact zone. In the derivation of the error estimator the local properties of the discontinuous solution are exploited appropriately so that, on the one hand, the error estimator has no contributions related to the non-linearity in the interior of the actual contact zone and, on the other hand, the critical region between the actual and non-actual contact zone can be well refined.
2710 (opens in new tab) 11.07.2016 Farwig, Reinhard
Giga, Yoshikazu
Hsu, Pen-Yuan
On the continuity of the solutions to the Navier-Stokes equations with initial data in critical Besov spaces MSC: 35Q30; 76D05
2709 (opens in new tab) 13.06.2016 Farwig, Reinhard
Giga, Yoshikazu
Hsu, Pen-Yuan
The Navier-Stokes equations with initial values in Besov spaces of type $B^{-1+3/q}_{q,\infty}$ MSC: 35A02; 35Q30; 76D03; 76D05
2708 (opens in new tab) 01.06.2016 Roch, Steffen Extension-restriction theorems for algebras of approximation sequences The $C^*$-algebra $S(T(C))$ of the finite sections discretization for Toeplitz operators with continuous generating function is fairly well understood.
Since its description in by Böttcher and Silbermann in 1983, this algebra had served both as a source of
inspiration and as an archetypal example of an algebra generated by an discretization procedure. The latter is no accident: it turns out that, after suitable extension by compact sequences and suitable fractal restriction, every separable $C^*$-algebra of approximation sequences has the same structure as $S(T(C))$. We explain what this statement means and give a proof.
2707 (opens in new tab) 13.04.2016 Farwig, Reinhard
Giga, Yoshikazu
Well-chosen Weak Solutions of the Instationary Navier-Stokes System and Their Uniqueness MSC: 35Q30; 35B65; 76D05; 76D03
We clarify the notion of well-chosen weak solutions of the instationary Navier-Stokes system recently introduced by the authors and P.-Y. Hsu in the article Initial values for the Navier-Stokes equations in spaces with weights in time, Funkcialaj Ekvacioj (2016). Well-chosen weak solutions have initial values in $L_\sigma^2(Ω)$ contained also in a quasi-optimal scalinginvariant space of Besov type such that nevertheless Serrin’s Uniqueness Theorem cannot be applied. However, we find universal conditions such that a weak solution given by a concrete approximation method coincides with the strong solution in a weighted function class of Serrin type.
2706 (opens in new tab) 02.03.2016 Ullmann, Sebastian
Rotkvic, Marko
Lang, Jens
POD-Galerkin reduced-order modeling with adaptive finite element snapshots We consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical issues arising from the fact that the snapshots are members of different finite element spaces. We propose a method to create a POD-Galerkin model without interpolating the snapshots onto their common finite element mesh. The error of the reduced-order solution is not necessarily Galerkin orthogonal to the reduced space created from space-adapted snapshot. We analyze how this influences the error assessment for POD-Galerkin models of linear elliptic boundary value problems. As a numerical example we consider a two-dimensional convection-diffusion equation with a parametrized convective direction. To illustrate the applicability of our techniques to non-linear timedependent problems, we present a test case of a two-dimensional viscous Burgers equation with parametrized initial data.
2705 (opens in new tab) 28.01.2016 Zahn, Peter Zur Widerspruchsfreiheit der Mengenlehre MSC: 03B10; 03C10; 03C62; 03E35; 03F50
2704 (opens in new tab) 14.01.2016 Roch, Steffen On Moore-Penrose ideals MSC: 46L05; 47A05
Every bounded linear operator on a Hilbert space which is invertible modulo compact operators has a closed range and is, thus, generalized invertible. We consider the analogue question in general $C^*$-algebras and describe the closed ideals (called Moore-Penrose ideals in what follows) with the property that whenever an element is invertible modulo that ideal, then it is generalized invertible. In particular, we will see that the class of Moore-Penrose ideals coincides with the class of the dual ideals. Finally, we study some questions related with the projection lifting property of Moore-Penrose ideals.
Number Date Author Title Abstract/MSC
2703 (opens in new tab) 191.12.2015 Maekawa, Yasunori
Sauer, Jonas
Maximal Regularity of the Time-Periodic Stokes Operator on Unbounded and Bounded Domains MSC: 35B10; 35B45; 35K59; 76D03; 76D07
We investigate the time-periodic Stokes equations with non-homogeneous divergence data in the whole space, the half space, bent half spaces and bounded domains. The solutions decompose into a well-studied stationary part and a purely periodic part, for which we establish $$L^p$ estimates. For
the whole space and the half space case we use a reduction of the Stokes equations to $(n − 1)$ heat equations. Perturbation and localisation methods yield the result on bent half spaces and bounded domains. A one-to-one correspondence between maximal regularity for the initial value problem and time periodic maximal regularity is proven, providing a short proof for the maximal regularity of the Stokes operator avoiding the notion of $R$-boundedness. The results are applied to a quasilinear model governing the
flow of nematic liquid crystals.
2702 (opens in new tab) 15.12.2015 Schröder, Dirk
Gerisch, Alf
Lang, Jens
Space-Time Adaptive Linearly Implicit Peer Methods for Parabolic Problems In this paper a linearly implicit peer method is combined with a multilevel finite element method for the discretization of parabolic partial differential equations. Following the Rothe method it is first discretized in time and then in space. A
spatial error estimator based on the hierarchical basis approach is derived. It is shown to be a reliable and efficient estimator up to some small perturbations. The efficiency index of the estimator is shown to be close to the ideal value one
for some one-dimensional test problems. Finally we compare the performance of the overall method, based on second, third, and fourth order peer methods with that of some Rosenbrock methods. We conclude that the presented peer methods offer an attractive alternative to Rosenbrock methods in this context.
2701 (opens in new tab) 11.12.2015 Roch, Steffen The universal algebra generated by a power partial isometry A power partial isometry (PPI) is an element v of a $C^*$-algebra with the property that every power $v^n$ iis a partial isometry. The goal of this paper is to identify the universal $C^*$-algebra generated by a PPI with
(a slight modification of) the algebra of the finite sections method for Toeplitz operators with continuous generating function, as first described by Albrecht B¨ottcher and Bernd Silbermann in 1983.
2700 (opens in new tab) 27.11.2015 Kyed, Mads
Sauer, Jonas
A Method for Obtaining Time-Periodic Lp Estimates MSC: 35B10; 35B45; 35K05
We introduce a method for showing a priori $L^p$ estimates for time-periodic, linear, partial differential equations set in a variety of domains such as the whole space, the half space and bounded domains. The method is generic and can be applied to a wide range of problems. We demonstrate it on the
heat equation. The main idea is to replace the time axis with a torus in order to reformulate the problem on a locally compact abelian group and to employ Fourier analysis on this group. As a by-product, maximal $L^p$ regularity for the corresponding initial-value problem follows without the notion of $R$-boundedness. Moreover, we introduce the concept of a timeperiodic fundamental solution.
2699 (opens in new tab) 07.07.2015 Alber, Hans-Dieter An alternative to the Allen-Cahn phase field model for interfaces in solids -- numerical efficiency MSC: 35B40; 35Q56; 35Q74; 74N20
2697 (opens in new tab) 28.04.2015 Alber, Hans-Dieter Asymptotics and numerical efficiency of the Allen-Cahn model for phase interfaces with low energy in solids MSC: 35B40; 35Q56; 35Q74; 74N20
The final publication appeared in Continuum Mech. Thermodyn., 29(3), 757-803, (2017). doi: 10.1007/s00161-017-0558-x
2698 (opens in new tab) 01.01.2015 Ewald, Tobias Convergence of Geometric Subdivision Schemes MSC: 26A15; 65D17
Number Date Author Title Abstract/MSC
2696 (opens in new tab) 11.12.2014 Farwig, Reinhard
Rosteck, Veronika
Resolvent estimates of the Stokes system with Navier boundary conditions in general unbounded domains MSC: 35Q30; 47A10; 76D07
Consider the Stokes resolvent system in general unbounded domains of uniform class C^3, and Navier slip boundary condition. The main result is the resolvent estimate in function spaces of the L^q-type adapted to the unboundedness of the domain. As a consequence we get that the Stokes operator generates an analytic semigroup.
2695 (opens in new tab) 19.11.2014 Hakenberg, Jan
Reif, Ulrich
On the Volume of Sets Bounded by Refinable Functions We present a method for the precise determination of the volume of subsets of R^d which are bounded by a hypersurface parametrized by a set of refinable functions. The derivation is based on the linear refinement equations rather than on closed form expressions of these functions, which may not be available. In particular, our approach makes it possible to compute the area of planar domains bounded by subdivision curves or the volume of spatial domains bounded by subdivision surfaces.
2694 (opens in new tab) 05.11.2014 Komo, Christian Strong solutions of the Boussinesq system in exterior domains 35Q35
We consider the instationary Boussinesq equations in a smooth three-dimensional exterior domain. A strong solution is a weak solution such that the velocity field additionally satisfies Serrin's condition. The crucial point in this concept of a strong solution is the fact that we have required no additional integrability condition for the temperature. We present a sufficient criterion for the existence of such a strong solution. Further we will characterize the class of initial values that allow the existence of such a strong solution in a sufficiently small interval. Finally we will obtain an uniqueness criterion for weak solutions of the Boussinesq equations which is based on the identification of a weak solution with a strong solution.
2693 (opens in new tab) 27.10.2014 Altherr, Lena C.
Ederer, Thorsten
Lorenz, Ulf
Pelz, Peter F.
Pöttgen, Philipp
Experimental Validation of an Enhanced System Synthesis Approach Optimizing the design and operating of a technical system is a common task for an engineer. Typically, the workflow is divided into two consecutive stages: First, a set-up is found by experience or by heuristic methods. Secondly, optimization techniques are used to compute an optimal usage strategy. This usually results in an optimal operating of a suboptimal system topology. In contrast, we apply Operations Research (OR) methods to find a cost-optimal solution for both stages simultaneously via mixed integer programming (MILP). Technical Operations Research (TOR) allows one to find a provable global optimal solution within the model formulation. However, the modeling error due to the abstraction of physical reality remains unknown. We address this ubiquitous problem of OR methods by comparing our computational results with measurements in a test rig. For a practical test case we compute a topology and control strategy via MILP and verify that the objectives are met up to a deviation of 8.7%.
2692 (opens in new tab) 22.10.2014 Farwig, Reinhard
Nakatsuka, Tomoyuki
Taniuchi, Yasushi
Existence of solutions on the whole time axis to the Navier-Stokes equations with precompact range in $L^3$ MSC: 35Q30; 35A01; 76D05
2691 (opens in new tab) 21.08.2014 Farwig, Reinhard
Giga, Yoshikazu
Hsu, Pen-Yuan
Initial values for the Navier-Stokes equations in spaces with weights in time
2690 (opens in new tab) 20.06.2014 Sauer, Jonas Maximal Regularity of the Spatially Periodic Stokes Operator and Application to Nematic Liquid Crystal Flows MSC: 35B10; 35K59; 35Q35; 76A15; 76D03
2689 (opens in new tab) 30.04.2014 Sauer, Jonas Weighted Resolvent Estimates for the Spatially Periodic Stokes Equations MSC: 35B10; 35Q30; 76D05
2688 (opens in new tab) 30.04.2014 Sauer, Jonas Extrapolation Theorem on Locally Compact Abelian Groups MSC: 42B25; 43A15; 43A70
2687 (opens in new tab) 01.04.2014 Ederer, Thorsten
Lorenz, Ulf
Opfer, Thomas
Quantified Combinatorial Optimization MIP and IP programming are state-of-the-art modeling techniques for computer-aided optimization. However, companies observe an increasing danger of disruptions that prevent them from acting as planned. One reason is input data being assumed as deterministic, but in reality, data is afflicted with uncertainties. Incorporating uncertainty in existing models, however, often pushes the complexity of problems that are in P or NP, to the complexity class PSPACE. Quantified integer linear programming (QIP) is a PSPACE-complete extension of the IP problem with variables being either existentially or universally quantified. With the help of QIPs, it is possible to model board-games like Gomoku as well as traditional combinatorial OR problems under uncertainty. In this paper, we present how to extend the model formulation of classical scheduling problems like the Job-Shop and Car-Sequencing problem by uncertain influences and give illustrating examples with solutions.
2686 (opens in new tab) 01.04.2014 Lorenz, Ulf
Opfer, Thomas
Wolf, Jan
Solution Techniques for Quantified Linear Programs and the links to Gaming Quantified linear programs (QLPs) are linear programs (LPs) with variables being either existentially or universally quantified. QLPs are two-person zero-sum games between an existential and a universal player on the one side, and convex multistage decision problems on the other side. Solutions of feasible QLPs are so called winning strategies for the existential player that specify how to react on moves – certain fixations of universally quantified variables – of the universal player to certainly win the game. To find a certain best one among different winning strategies, we propose the extension of the QLP decision problem by an objective function. To solve the resulting QLP optimization problem, we exploit the problem’s hybrid nature and combine linear programming techniques with solution techniques from game-tree search. As a result, we present an extension of the Nested Benders Decomposition algorithm by the αβ-heuristic and move-ordering, two techniques that are used in game-tree search to solve minimax trees. The principle applicability of our method to both QLPs and QIP models of PSPACE-complete games like Connect6 is examined in an experimental evaluation.
2685 (opens in new tab) 27.03.2014 Ederer, Thorsten A Quantified Mixed-Integer Program for a Booster Station A booster station is a component in a fluid network which can cause a pressure increase. This component may be a single pump or rather a subnetwork of multiple pumps. If the pumps are not operated in sync and if at most one of these pumps is speed-controlled, the booster station can be regarded as a black box pump with a compound head curve. However, such a booster station is no improvement over a single pump with the same head curve. (A single large pump may even be more efficient due to scaling laws.) Thus, the advantage of a booster station over a single pump consists in the freedom to deactivate individual pumps or to speed-control more than one pump, such that the active pumps may operate near their optimal working point. If the average demand of volume flow or pressure head is significantly smaller than the maximal demand, the system developer might therefore provide two or three smaller pumps in parallel or respectively serial connection. The difficulty is that system developer has to make his decision about the system topology in advance. Therefore, the full task is: ’Find a valid flexible topology of pumps such that the investment costs plus the expected operating costs over a certain time are minimized’. Moreover, the pump system should work for nearly all possible load demands, even if the cost minimization is based on only a couple of some few predefined load scenarios.
2684 (opens in new tab) 24.03.2014 Farwig, Reinhard
Paul Felix Riechwald
Very weak solutions and the Fujita-Kato approach to the Navier-Stokes system in general unbounded domains MSC: 35B65; 76D05; 76D03
2683 (opens in new tab) 10.03.2014 Ri Myong-Hwan
Farwig, Reinhard
Resolvent Estimates and Maximal Regularity in Weighted Lebesgue Spaces of the Stokes Operator in Unbounded Cylinders MSC: 35Q30; 76D05; 76D07
2682 (opens in new tab) 25.02.2014 Farwig, Reinhard
Pokorny, Milan
A Linearized Model for Compressible Flow past a Rotating Obstacle: Analysis via Modified Bochner-Riesz Multipliers MSC: 35Q35; 42A45; 76N10
Consider the flow of a compressible Newtonian fluid around or past a rotating rigid obstacle in R^3. After a coordinate transform to get a problem in a time-independent domain we assume the new system to be stationary, then linearize and use Fourier transform to prove the existence of a unique solution in L^q-spaces. However, in contrast to the incompressible case with multipliers based on the heat kernel the new multiplier functions are related to Bochner-Riesz multipliers and require the restriction 6/5<q<6.
2681 (opens in new tab) 24.02.2014 Farwig, Reinhard
Riechwald, Felix
Very weak solutions to the Navier-Stokes system in general unbounded domains MSC: 35B65; 76D05; 76D03
2680 (opens in new tab) 28.01.2014 Komo, Christian Uniqueness criteria and strong solutions of the Boussinesq equations in completely general domains MSC: 35Q35; 76D03
2679 (opens in new tab) 22.01.2014 Ewald, Tobias
Reif, Ulrich
Sabin, Malcolm
Hölder Regularity of Geometric Subdivision Schemes
2678 (opens in new tab) 21.01.2014 Roch, Steffen Finite sections of truncated Toeplitz operators MSC: 65J10; 46L99; 47N40
Number Date Author Title Abstract/MSC
2677 (opens in new tab) 18.12.2013 Giga, Yoshikazu
Sauer, Jonas
Schade, Katharina
Strong Stability of 2D Viscoelastic Poiseuille-Type Flows MSC: 35A01; 35A02; 35Q35; 76A05; 76A10; 76D03; 35K59
2676 (opens in new tab) 05.12.2013 Farwig, Reinhard
Sohr, Hermann
Varnhorn, Werner
Local strong solutions of the nonhomogeneous Navier-Stokes system with control of the interval of existence MSC: 35Q30; 76D05
2675 (opens in new tab) 24.11.2013 Farwg, Reinhard
Taniuchi, Yasushi
Nakatsuka, Tomoyuki
Uniqueness of solutions on the whole time axis to the Navier-Stokes equations in unbounded domains MSC: 35Q30; 35A02; 76D05
2674 (opens in new tab) 19.11.2013 Reif, Ulrich
Sissouno, Nada
Approximation with Diversified B-Splines
2673 (opens in new tab) 19.11.2013 Komo, Christian Influence of surface roughness to solutions of the Boussinesq equations with Robin boundary condition MSC: 35Q35; 76D99
2672 (opens in new tab) 22.10.2013 Komo, Christian Optimal initial value conditions for the existence of strong solutions of the Boussinesq equations MSC: 35Q35; 76D03
2671 (opens in new tab) 18.09.2013 Farwig, Reinhard On regularity of weak solutions to the instationary Navier-Stokes system – a review on recent results MSC: 35B65; 76D05; 76D03
2670 (opens in new tab) 11.09.2013 Komo, Christian Necessary and sufficient conditions for local strong solvability of the Navier-Stokes equations in exterior domains
2669 (opens in new tab) 10.09.2013
Farwig, Reinhard
Sohr, Hermann
Varnhorn, Werner
Besov space regularity conditions for weak solutions of the Navier-Stokes equations MSC: 35Q30; 76D03; 76D05
2668 (opens in new tab) 10.07.2013 Farwig,Reinhard
Kozono, Hideo
Weak Solutions of the Navier-Stokes Equations with Non-zero Boundary Values in an Exterior Domain Satisfying the Strong Energy Inequality MSC: 35Q30; 35J65; 76D05
2667 (opens in new tab) 25.06.2013 Ederer, Thorsten
Lorenz, Ulf
Opfer, Thomas
Wolf, Jan
An algorithmic framework for 0/1-QIP solvers Quantified linear programs (QLPs) are linear programs with variables being either existentially or universally quantified. The integer variant (QIP) is PSPACE-complete, and the problem is similar to games like chess, where an existential and a universal player have to play a two-person-zero-sum game. We present the algorithmic concepts of our solver Yasol which solves multistage 0/1-QIPs to optimality with up to several hundred existential and two dozens of universal variables. Being a mixture of a QSAT solver and a branch&cut IP-solver, Yasols opens a new category of quantifier-extended IP solvers.
2666 (opens in new tab) 03.05.2013 Moeller, Claudia
Reif, Ulrich
A Tree-Based Approach to Joint Spectral Radius Determination MSC: 15A18; 15A60
2665 (opens in new tab) 27.03.2013 Alber, Hans-Dieter The continuous theory of dislocations for a material containing dislocations to one Burgers vector only MSC: 35Q74; 74A60
74C10
2664 (opens in new tab) 21.03.2013 Roch, Steffen
Santos. Pedro A.
A tour to compact type operators and sequences related to the finite sections projection MSC: 65R20; 45E10; 47B35; 47L80; 65J10
2663 (opens in new tab) 21.03.2013 Roch, Steffen
Santos, Pedro A.
Finite section approximation in an algebra of convolution, multiplication and flip operators on $L^p({\mathbb R})$ MSC: 65J10
2662 (opens in new tab) 11.02.2013 Ederer, Thorsten
Avemann, Jörg
Schmitt, Sebastian O.
Lorenz, Ulf
Groche, Peter
Assessment of Flexibility in Forming Technology in an Uncertain Sales Market Framework
2661 (opens in new tab) 06.02.2013 Farwig, Reinhard
Sauer, Jonas
Very Weak Solutions of the Stationary Stokes Equations on Unbounded Domains of Half Space Type MSC: 76D05; 35Q30; 35J65
2660 (opens in new tab) 19.04.2013 Lorenz, Ulf
Wolf,Jan
Solving Multistage Quantified Linear Optimization Problems with the Alpha-Beta Nested Benders Decomposition
2659 (opens in new tab) 04.01.2013 Nesenenko, Sergiy
Neff, Patrizio
Homogenization for dislocation based gradient visco-plasticity MSC: 35B65; 35D10; 74C10; 74D10; 35J25; 34G20; 34G25; 47H04; 47H05
Number Date Author Title Abstract/MSC
2658 (opens in new tab) 16.10.2012 Clever, Debora Analysis for an SP$_1$-N$_\nu$?-band model in radiative heat transfer
2657 (opens in new tab) 08.10.2012 Clever, Debora
Lang, Jens
Multilevel optimization for PDAE-constrained optimal control problems with pointwise constraints on control and state
2656 (opens in new tab) 24.08.2012 Kraynyukova, Nataliya
Nesenenko, Sergiy
Measure-valued solutions for models of ferroelectric material behavior
2655 (opens in new tab) 27.07.2012 Farwig, R.
Guenther, R.B., Necasova, S., Thomann, E.A.
The Fundamental Solution of Linearized Nonstationary Navier-Stokes Equations of Motion around a Rotating and Translating Body MSC: 35Q30; 35Q35; 76D05; 76D07
We derive the fundamental solution of the linearized problem of the motion of a viscous fluid around a rotating body when the axis of rotation of the body is not parallel to the velocity of the fluid at infinity.
2654 (opens in new tab) 01.06.2012 Maksym, Berezhnyi
Eugen Khruslov
Asymmetric hydrodynamics of suspensions. Nonlinear case.
2650 (opens in new tab) 27.06.2012 Ederer, Thorsten
Lorenz, Ulf
Martin, Alexander
Opfer, Thomas
Wolf, Jan
Polyhedral Properties and Algorithmic Aspects of Quantified Linear Programs
2653 (opens in new tab) 31.05.2012 Ullmann, Sebastian
Löbig, Stefan
Lang, Jens
Adaptive Large Eddy Simulation and Reduced-Order Modeling MSC: 76F65; 76M12; 76M10; 76M25
2652 (opens in new tab) 21.05.2012 Nesenenko, Sergiy
Neff, Patrizio
Well-posedness for dislocation based gradient visco-plasticity II: monotone case
2651 (opens in new tab) 18.04.2012 Schulz, Raphael Spatial Asymptotic Profiles of Solutions of the Navier-Stokes System in a Rotating Frame MSC: 76U05; 76D05; 35Q30; 35Q35
2649 (opens in new tab) 06.03.2012 Farwig, Reinhard
Schulz, Raphael
Yamazaki, Masao
Concentration-Diffusion Phenomena of Heat Convection in an Incompressible Fluid MSC: 76D05; 35K05; 35Q30; 35Q35
2648 (opens in new tab) 31.01.2012 Berezhnyi, Maksym Asymmetric hydrodynamics of suspensions subjected to the influence of strong external magnetic fields A viscous incompressible fluid with a large number of small axially symmetric solid particles is considered. It is assumed that the particles are identically oriented and under the influence of the fluid they move translationally or rotate around symmetry axis but the direction of their symmetry axes does not change. The asymptotic behavior of small oscillations of the system is studied, when the diameters of particles and distances between the nearest particles are decreased. The equations, describing the homogenized model of the system, are derived. It is shown that the homogenized equations correspond to a non-standard hydrodynamics. Namely, the homogenized stress tensor linearly depends not only on the strain tensor but also on the rotation tensor.
2647 (opens in new tab) 17.01.2012 Kozono, Hideo
Ushikoshi, Erika
Hadamard variational formula for the Green function of the boundary value problem on the Stokes equations MSC: 35Q30; 35J25; 35C20; 76D07
Number Date Author Title MSC
2645 (opens in new tab) 20.12.2011 Clever, Debora
Lang, Jens
Schröder, Dirk
Model Hierarchy Based Optimal Control of Radiative Heat Transfer
2644 (opens in new tab) 14.12.2011 Roch, Steffen
Silbermann, Bernd
A handy formula for the Fredholm index of Toeplitz plus Hankel operators 47B35
47B48
2646 (opens in new tab) 16.01.2012 Fischer, André
Saal, Jürgen
On instability of the Ekman spiral
2643 (opens in new tab) 07.11.2011 Riechwald, Paul Felix Interpolation of sum and intersection spaces of $L^q$-type and applications to the Stokes problem in general unbounded domains 46B70
35Q30
2642 (opens in new tab) 05.10.2011 Roch, Steffen
Santos, Pedro A.
Two points, one limit: Homogenization techniques for two-point local algebras 47L15
45E10
47B35
47C05
2641 (opens in new tab) 08.09.2011 Alber, Hans-Dieter A model for brittle fracture based on the hybrid phase field model publication (opens in new tab)
35Q72
35K65
74R10
2640 (opens in new tab) 26.08.2011 Kyed, Mads On a mapping property of the Oseen operator with rotation 35Q30
35B40
35C20
76D05
2639 (opens in new tab) 26.08.2011 Kyed, Mads On the Asymptotic Structure of a Navier-Stokes Flow Past a Rotating Body 35Q30
35B40
35C20
76D05
2638 (opens in new tab) 26.08.2011 Kyed, Mads Asymptotic Profile of a Linearized Navier-Stokes Flow Past a Rotating Body 35Q30
76D05
35B40
35C20
2637 (opens in new tab) 26.08.2011 Giovanni P. Galdi
Kyed, Mads
A simple proof of Lq-estimates for the steady-state Oseen and Stokes equations in a rotating frame. Part II: Weak solutions 35Q30
35B45
76D07
2636 (opens in new tab) 26.08.2011 Giovanni P. Galdi
Kyed, Mads
A simple proof of Lq-estimates for the steady-state Oseen and Stokes equations in a rotating frame. Part I: Strong solutions 35Q30
35B45
76D07
2635 (opens in new tab) 23.08.2011 Roch, Steffen Fractal algebras of discretization sequences
2634 (opens in new tab) 06.07.2011 Sawada, Okihiro Term-wise estimates for the norm inflation solutions to the Navier-Stokes equations
2633 (opens in new tab) 22.06.2011 Rabinovich, Vladimir
Roch, Steffen
Pseudodifferential operators on periodic graphs
2632 (opens in new tab) 21.06.2011 Roch, Steffen Arveson dichotomy and essential fractality
2631 (opens in new tab) 01.06.2011 Alber, Hans-Dieter
Zhu, Peicheng
Comparison of a rapidely converging phase field model for interfaces in solids with the Allen-Cahn model publication (opens in new tab)
35Q72
35K65
74N20
2630 (opens in new tab) 12.05.2011 Komo, Christian Convergence Properties of weak solutions of the Boussinesq equations in domains with rough boundaries 35Q35
2629 (opens in new tab) 09.05.2011 Farwig, Reinhard
Neustupa, Jiri
Penel, Patrick
Vorticity, Rotation and Symmetry (II – Regularity of Fluid Motion)
2628 (opens in new tab) 28.04.2011 Lang, Jens
Verwer, Jan
W-Methods in Optimal Control 34H05
49J15
65L05
65L06
2627 (opens in new tab) 18.04.2011 Davydov, Oleg
Prasiswa, Jennifer
Reif, Ulrich
Two-Stage Approximation Methods with Extended B-Splines 41A15
65D07
2626 (opens in new tab) 13.04.2011 Farwig, Reinhard
Komo, Christian
Optimal initial value conditions for local strong solutions of the Navier-Stokes equations in exterior domains 76D05
35Q30
35B65
2625 (opens in new tab) 15.02.2011 Kuhn, Karen
Lang, Jens
Comparison of asymptotic stability for recursive ROS-multirate methods