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Global existence for a nonlinear system in thermoviscoelasticity with nonconvex energy


Reference:

Zimmer, J., 2004. Global existence for a nonlinear system in thermoviscoelasticity with nonconvex energy. Journal of Mathematical Analysis and Applications, 292 (2), pp. 589-604.

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Official URL:

http://dx.doi.org/10.1016/j.jmaa.2003.12.010

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.

Details

Item Type Articles
CreatorsZimmer, J.
DOI10.1016/j.jmaa.2003.12.010
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code7192
Additional InformationID number: ISI:000221110800021

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