Currently displaying 1 – 20 of 21

Showing per page

Order by Relevance | Title | Year of publication

Unconditional stability of difference formulas

Tomáš Roubíček — 1983

Aplikace matematiky

The paper concerns the solution of partial differential equations of evolution type by the finite difference method. The author discusses the general assumptions on the original equation as well as its discretization, which guarantee that the difference scheme is unconditionally stable, i.e. stable without any stability condition for the time-step. A new notion of the A n -acceptability of the integration formula is introduced and examples of such formulas are given. The results can be applied to ordinary...

Constrained optimization: A general tolerance approach

Tomáš Roubíček — 1990

Aplikace matematiky

To overcome the somewhat artificial difficulties in classical optimization theory concerning the existence and stability of minimizers, a new setting of constrained optimization problems (called problems with tolerance) is proposed using given proximity structures to define the neighbourhoods of sets. The infimum and the so-called minimizing filter are then defined by means of level sets created by these neighbourhoods, which also reflects the engineering approach to constrained optimization problems....

On noncooperative nonlinear differential games

Tomáš Roubíček — 1999

Kybernetika

Noncooperative games with systems governed by nonlinear differential equations remain, in general, nonconvex even if continuously extended (i. e. relaxed) in terms of Young measures. However, if the individual payoff functionals are “enough” uniformly convex and the controlled system is only “slightly” nonlinear, then the relaxed game enjoys a globally convex structure, which guarantees existence of its Nash equilibria as well as existence of approximate Nash equilibria (in a suitable sense) for...

Optimality conditions for nonconvex variational problems relaxed in terms of Young measures

Tomáš Roubíček — 1998

Kybernetika

The scalar nonconvex variational problems of the minimum-energy type on Sobolev spaces are studied. As the Euler–Lagrange equation dramatically looses selectivity when extended in terms of the Young measures, the correct optimality conditions are sought by means of the convex compactification theory. It turns out that these conditions basically combine one part from the Euler–Lagrange equation with one part from the Weierstrass condition.

Nonconcentrating generalized Young functionals

Tomáš Roubíček — 1997

Commentationes Mathematicae Universitatis Carolinae

The Young measures, used widely for relaxation of various optimization problems, can be naturally understood as certain functionals on suitable space of integrands, which allows readily various generalizations. The paper is focused on such functionals which can be attained by sequences whose “energy” (= p th power) does not concentrate in the sense that it is relatively weakly compact in L 1 ( Ω ) . Straightforward applications to coercive optimization problems are briefly outlined.

Relaxation of vectorial variational problems

Tomáš Roubíček — 1995

Mathematica Bohemica

Multidimensional vectorial non-quasiconvex variational problems are relaxed by means of a generalized-Young-functional technique. Selective first-order optimality conditions, having the form of an Euler-Weiestrass condition involving minors, are formulated in a special, rather a model case when the potential has a polyconvex quasiconvexification.

Steady-state buoyancy-driven viscous flow with measure data

Tomáš Roubíček — 2001

Mathematica Bohemica

Steady-state system of equations for incompressible, possibly non-Newtonean of the p -power type, viscous flow coupled with the heat equation is considered in a smooth bounded domain Ω n , n = 2 or 3, with heat sources allowed to have a natural L 1 -structure and even to be measures. The existence of a distributional solution is shown by a fixed-point technique for sufficiently small data if p > 3 / 2 (for n = 2 ) or if p > 9 / 5 (for n = 3 ).

Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion

Sören BartelsTomáš Roubíček — 2011

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider a viscoelastic solid in Kelvin-Voigt rheology exhibiting also plasticity with hardening and coupled with heat-transfer through dissipative heat production by viscoplastic effects and through thermal expansion and corresponding adiabatic effects. Numerical discretization of the thermodynamically consistent model is proposed by implicit time discretization, suitable regularization, and finite elements in space. Fine estimates are derived, and convergence is proved by careful successive...

Approximation of a nonlinear thermoelastic problem with a moving boundary via a fixed-domain method

Jindřich NečasTomáš Roubíček — 1990

Aplikace matematiky

The thermoelastic stresses created in a solid phase domain in the course of solidification of a molten ingot are investigated. A nonlinear behaviour of the solid phase is admitted, too. This problem, obtained from a real situation by many simplifications, contains a moving boundary between the solid and the liquid phase domains. To make the usage of standard numerical packages possible, we propose here a fixed-domain approximation by means of including the liquid phase domain into the problem (in...

On the measures of DiPerna and Majda

Martin KružíkTomáš Roubíček — 1997

Mathematica Bohemica

DiPerna and Majda generalized Young measures so that it is possible to describe “in the limit” oscillation as well as concentration effects of bounded sequences in L p -spaces. Here the complete description of all such measures is stated, showing that the “energy” put at “infinity” by concentration effects can be described in the limit basically by an arbitrary positive Radon measure. Moreover, it is shown that concentration effects are intimately related to rays (in a suitable locally convex geometry)...

Numerical approaches to rate-independent processes and applications in inelasticity

Alexander MielkeTomáš Roubíček — 2009

ESAIM: Mathematical Modelling and Numerical Analysis

A conceptual numerical strategy for rate-independent processes in the energetic formulation is proposed and its convergence is proved under various rather mild data qualifications. The novelty is that we obtain convergence of subsequences of space-time discretizations even in case where the limit problem does not have a unique solution and we need no additional assumptions on higher regularity of the limit solution. The variety of general perspectives thus obtained is illustrated on several...

Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion

Sören BartelsTomáš Roubíček — 2011

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a viscoelastic solid in Kelvin-Voigt rheology exhibiting also plasticity with hardening and coupled with heat-transfer through dissipative heat production by viscoplastic effects and through thermal expansion and corresponding adiabatic effects. Numerical discretization of the thermodynamically consistent model is proposed by implicit time discretization, suitable regularization, and finite elements in space. Fine estimates are derived, and convergence is proved by careful successive...

Page 1 Next

Download Results (CSV)