# American Institute of Mathematical Sciences

December  2003, 2(4): 495-509. doi: 10.3934/cpaa.2003.2.495

## On the compactness of the stable set for rate independent processes

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

Received  April 2003 Revised  August 2003 Published  October 2003

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.
Citation: M. A. Efendiev. On the compactness of the stable set for rate independent processes. Communications on Pure & Applied Analysis, 2003, 2 (4) : 495-509. doi: 10.3934/cpaa.2003.2.495
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