MiS Preprint Repository

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MiS Preprint

Global Existence for a Nonlinear System in Thermoviscoelasticity with Nonconvex Energy

Johannes Zimmer


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 $L^1$ data.

MSC Codes:
35Q72, 35D05, 73B30, 35M20, 73F15

Related publications

2004 Repository Open Access
Johannes Zimmer

Global existence for a nonlinear system in thermoviscoelasticity with nonconvex energy

In: Journal of mathematical analysis and applications, 292 (2004) 2, pp. 589-604