Evolution equations of second order with nonconvex potential and linear damping: existence via convergence of a full discretization

Etienne Emmrich, David Siska

Research output: Contribution to journalArticlepeer-review

Abstract

Global existence of solutions for a class of second-order evolution equations with damping is shown by proving convergence of a full discretization. The discretization combines a fully implicit time stepping with a Galerkin scheme. The operator acting on the zero-order term is assumed to be a potential operator where the potential may be nonconvex. A linear, symmetric operator is assumed to be acting on the first-order term. Applications arise in nonlinear viscoelasticity and elastodynamics. (C) 2013 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)3719-3746
Number of pages28
JournalJournal of Differential Equations
Volume255
Issue number10
DOIs
Publication statusPublished - 15 Nov 2013

Keywords

  • Evolution equation of second order
  • Elastodynamics
  • Nonconvex potential
  • Full discretization
  • Convergence
  • SHAPE-MEMORY ALLOYS
  • GLOBAL REGULAR SOLUTIONS
  • FINITE-ELEMENT SPACES
  • TIME DISCRETIZATION
  • NONLINEAR VISCOELASTICITY
  • DIFFERENTIAL-EQUATIONS
  • PHASE-TRANSITIONS
  • WEAK SOLUTIONS
  • ELASTODYNAMICS
  • STABILITY

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