Global Existence for a Nonlinear System in Thermoviscoelasticity with Nonconvex Energy
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Submission date: 08. Dec. 2003
published in: Journal of mathematical analysis and applications, 292 (2004) 2, p. 589-604
DOI number (of the published article): 10.1016/j.jmaa.2003.12.010
MSC-Numbers: 35Q72, 35D05, 73B30, 35M20, 73F15
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A three-dimensional thermoviscoelastic 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 multi-dimensional, nonconvex, and non-isothermal 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 data.