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Dynamical modelling of phase transitions by means of viscoelasticity in many dimensions. (English) Zbl 0758.73004
Summary: We study the equations of viscoelasticity in a multidimensional setting for the ‘no-traction’ boundary data. For the sake of modelling phase transitions we do not assume ellipticity of the stored energy function \(W\). We construct dynamics in \(W^{1,2}(\Omega;\mathbb{R}^ n)\) globally in time. Next, we study the question of stability for a class of equilibria. Moreover, we show a certain kind of decay in time of solutions for arbitrary initial conditions.

MSC:
74A15 Thermodynamics in solid mechanics
74Hxx Dynamical problems in solid mechanics
80A22 Stefan problems, phase changes, etc.
35Q72 Other PDE from mechanics (MSC2000)
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