Displaying similar documents to “Numerical approximations of the relative rearrangement : the piecewise linear case. Application to some nonlocal problems”

On the worst scenario method: a modified convergence theorem and its application to an uncertain differential equation

Petr Harasim (2008)

Applications of Mathematics

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We propose a theoretical framework for solving a class of worst scenario problems. The existence of the worst scenario is proved through the convergence of a sequence of approximate worst scenarios. The main convergence theorem modifies and corrects the relevant results already published in literature. The theoretical framework is applied to a particular problem with an uncertain boundary value problem for a nonlinear ordinary differential equation with an uncertain coefficient. ...

Young-measure approximations for elastodynamics with non-monotone stress-strain relations

Carsten Carstensen, Marc Oliver Rieger (2004)

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

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Microstructures in phase-transitions of alloys are modeled by the energy minimization of a nonconvex energy density φ . Their time-evolution leads to a nonlinear wave equation u t t = div S ( D u ) with the non-monotone stress-strain relation S = D φ plus proper boundary and initial conditions. This hyperbolic-elliptic initial-boundary value problem of changing types allows, in general, solely Young-measure solutions. This paper introduces a fully-numerical time-space discretization of this equation in a corresponding...