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Dynamical modelling of phase transitions by means of viscoelasticity in many dimensions

Published online by Cambridge University Press:  14 November 2011

Piotr Rybka
Piotr Rybka
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A
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Synopsis

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 elliptieity of the stored energy function W. We construct dynamics in W1,2(Ωℝn) 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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 121 , Issue 1-2 , 1992 , pp. 101 - 138
Copyright
Copyright © Royal Society of Edinburgh 1992

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