O. Klein, Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin, Germany, e-mail: klein@wias-berlin.de
Abstract: The asymptotic behaviour for $t \to\infty$ of the solutions to a one-dimensional model for thermo-visco-plastic behaviour is investigated in this paper. The model consists of a coupled system of nonlinear partial differential equations, representing the equation of motion, the balance of the internal energy, and a phase evolution equation, determining the evolution of a phase variable. The phase evolution equation can be used to deal with relaxation processes. Rate-independent hysteresis effects in the strain-stress law and also in the phase evolution equation are described by using the mathematical theory of hysteresis operators.
Keywords: phase-field system, phase transition, hysteresis operator, thermo-visco-plasticity, asymptotic behaviour
Classification (MSC 2000): 74N30, 35B40, 47J40, 34C55, 35K60, 74K05
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