Global existence for a nonlinear system in thermoviscoelasticity with nonconvex energy

J Zimmer

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13 Citations (Scopus)
123 Downloads (Pure)

Abstract

A three-dimensional thermoviscoclastic system derived from the balance laws of momentum and energy is considered. To describe structural phase transitions in solids, the stored energy function is not assumed to be convex as a function of the deformation gradient. A novel feature for multidimensional, nonconvex, and nonisothermal problems is that no regularizing higher-order terms are introduced. The mechanical dissipation is not linearized. We prove existence global in time. The approach is based on a fixed-point argument using an implicit time discretization and the theory of renormalized solutions for parabolic equations with L-1 data. (C) 2004 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)589-604
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Volume292
Issue number2
Early online date25 Feb 2004
DOIs
Publication statusPublished - 15 Apr 2004

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