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Title: Homogenization of diffusion equation with scalar hysteresis operator (English)
Author: Franců, Jan
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 126
Issue: 2
Year: 2001
Pages: 363-377
Summary lang: English
Category: math
Summary: The paper deals with a scalar diffusion equation $ c\,u_t = ({{F}}[u_x])_x + f, $ where ${F}$ is a Prandtl-Ishlinskii operator and $c, f$ are given functions. In the diffusion or heat conduction equation the linear constitutive relation is replaced by a scalar Prandtl-Ishlinskii hysteresis spatially dependent operator. We prove existence, uniqueness and regularity of solution to the corresponding initial-boundary value problem. The problem is then homogenized by considering a sequence of equations of the above type with spatially periodic data $c^\varepsilon $ and $\eta ^\varepsilon $ when the spatial period $\varepsilon $ tends to zero. The homogenized characteristics $c^*$ and $\eta ^*$ are identified and the convergence of the corresponding solutions to the solution of the homogenized equation is proved. (English)
Keyword: hysteresis
Keyword: Prandtl-Ishlinskii operator
Keyword: material with periodic structure
Keyword: nonlinear diffusion equation
Keyword: homogenization
Keyword: initial-boundary value problem
Keyword: spatially periodic data
MSC: 34C55
MSC: 35B27
MSC: 47J40
idZBL: Zbl 0977.35017
idMR: MR1844275
DOI: 10.21136/MB.2001.134031
Date available: 2009-09-24T21:51:33Z
Last updated: 2020-07-29
Stable URL:
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