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Evolution equations of second order with nonconvex potential and linear damping: existence via convergence of a full discretization. (English) Zbl 1317.47067
Summary: 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.

MSC:
47J35 Nonlinear evolution equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
34G20 Nonlinear differential equations in abstract spaces
35G25 Initial value problems for nonlinear higher-order PDEs
35Q74 PDEs in connection with mechanics of deformable solids
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