Geodesic
Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity
Applications of Mathematics, Tome 49 (2004) no. 4, pp. 309-341.

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The asymptotic behaviour for $t \rightarrow \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.
DOI : 10.1007/s10492-004-6402-1
Classification : 34C55, 35B40, 35K60, 47J40, 74K05, 74N30
Keywords: phase-field system; phase transition; hysteresis operator; thermo-visco-plasticity; asymptotic behaviour 
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     title = {Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity},
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Klein, Olaf. Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity. Applications of Mathematics, Tome 49 (2004) no. 4, pp. 309-341. doi : 10.1007/s10492-004-6402-1. http://geodesic.mathdoc.fr/articles/10.1007/s10492-004-6402-1/

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