On the compactness of the stable set for rate independent processes

M. A. Efendiev

doi:10.3934/cpaa.2003.2.495

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2003, Volume 2, Issue 4: 495-509. Doi: 10.3934/cpaa.2003.2.495

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On the compactness of the stable set for rate independent processes

M. A. Efendiev^1,

1.
Mathematisches Institut A, Universitat Stuttgart, D-70569 Stuttgart

Received: March 31, 2003

Revised: July 31, 2003

Published: November 2003

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Abstract

This paper deals with a general approach to the rate-independent processes which may display hysteretic behaviour.This approach based on the two energy functionals,namely potential and dissipation functionals.Under some natural assumptions on these functionals we prove the compactness of the set of stable points which in turn leads to the existence of solutions of the problems under consideration.We present an application of our results to ferromagnetic models.

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Mathematics Subject Classification: 47J20, 49K20, 47H11.

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