Homogenization of heat equation with hysteresis

The contribution deals with heat equation in the form (c u+W[u]) t= div(a·∇u)+f , where the nonlinear functional operator W[ u] is a Prandtl–Ishlinskii hysteresis operator of play type characterized by a distribution function η. The spatially dependent initial boundary value problem is studied. Proo...

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Bibliographic Details
Published in:Mathematics and computers in simulation 2003-01, Vol.61 (3), p.591-597
Main Author: Franců, Jan
Format: Article
Language:English
Subjects:
Heat equation
Homogenization
Prandtl–Ishlinskii operator
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Summary:The contribution deals with heat equation in the form (c u+W[u]) t= div(a·∇u)+f , where the nonlinear functional operator W[ u] is a Prandtl–Ishlinskii hysteresis operator of play type characterized by a distribution function η. The spatially dependent initial boundary value problem is studied. Proof of existence and uniqueness of the solution is omitted since the proof is a slightly modified proof by Brokate–Sprekels. The homogenization problem for this equation is studied. For ε→0, a sequence of problems of the above type with spatially ε-periodic coefficients c ε , η ε , a ε is considered. The coefficients c *, η * and a * in the homogenized problem are identified and convergence of the corresponding solutions u ε to u * is proved.
ISSN:0378-4754
1872-7166
DOI:10.1016/S0378-4754(02)00110-6