Homogenization of heat equation with hysteresis
type: Item
instance of: scholarly article
title: Homogenization of heat equation with hysteresis
zbMATH Open document ID: 1021.35008
DOI: 10.1016/S0378-4754(02)00110-6
published in: Mathematics and Computers in Simulation
publication date: 2003-03-16T00:00:00Z
review text: This paper is devoted to the homogenization problem for the heat equation in a higher dimension in the form \[ (cu+W[u])_t-\text{div}(a\cdot \nabla u)=f,\tag{1} \] with scalar hypothesis operator \(W\) characterized by a coefficient \(\eta\). Here the coefficients \(c\), \(\eta\), \(a\) are spatially dependent. The authors prove that the solutions \(u^\varepsilon\) of \[ (c^\varepsilon u^\varepsilon+W^\varepsilon[u^\varepsilon])_t-\text{div}(a^\varepsilon\cdot\nabla u^\varepsilon)=f^\varepsilon \tag{2} \] with \(\varepsilon\)-periodic data converge to a solution \(u^*\) of a problem of the same form.
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1882296
zbMATH Keywords: Prandtl-Ishlinksii operator
zbMATH Keywords: periodic data
author: Jan Franců
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Homogenization and Two-Scale Convergence
cites work: Q4189539
cites work: Q4389324
cites work: Hysteresis and phase transitions
cites work: Homogenization of scalar wave equations with hysteresis
cites work: Homogenization of diffusion equation with scalar hysteresis operator
cites work: On two-scale convergence
cites work: Q4365247
cites work: Differential models of hysteresis
full work available at URL: s0378-4754(02)00110-6
OpenAlex ID: W2104761058
description: scientific article; zbMATH DE number 1882296