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December  2007, 6(4): 1131-1143. doi: 10.3934/cpaa.2007.6.1131

An asymptotic convergence result for a system of partial differential equations with hysteresis

Michela Eleuteri 1, and  Pavel Krejčí 2,

1. 

Università degli Studi di Trento, Dipartimento di Matematica, Via Sommarive 14, I–38050 Povo (Trento)
2. 

Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D–10117 Berlin

Received  October 2006 Revised  March 2007 Published  September 2007

A partial differential equation motivated by electromagnetic field equations in ferromagnetic media is considered with a relaxed rate dependent constitutive relation. It is shown that the solutions converge to the unique solution of the limit parabolic problem with a rate independent Preisach hysteresis constitutive operator as the relaxation parameter tends to zero.
Keywords: hysteresis, Partial differential equations, asymptotic convergence, Preisach operator..
Mathematics Subject Classification: 35K55, 47J40, 35B4.
Citation: Michela Eleuteri, Pavel Krejčí. An asymptotic convergence result for a system of partial differential equations with hysteresis. Communications on Pure & Applied Analysis, 2007, 6 (4) : 1131-1143. doi: 10.3934/cpaa.2007.6.1131
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