The asymptotic expansion of the solution to the Cauchy problem for a parabolic equation in a perforated space
type: Item
instance of: scholarly article
title: The asymptotic expansion of the solution to the Cauchy problem for a parabolic equation in a perforated space
zbMATH Open document ID: 0917.35009
DOI: 10.1007/BF02355840
published in: Journal of Mathematical Sciences (New York)
publication date: 1999-03-15T00:00:00Z
review text: In this paper the author deals with the Cauchy problem for a second order parabolic equation: \[ {{\partial u_\varepsilon}\over{\partial t}} - {{\partial}\over{\partial x_i}} \bigl( a_{ij}(\varepsilon^{-1}x,\varepsilon^{-2k} t) {{\partial u_\varepsilon}\over{\partial x_j}} \bigr) = f, \] where \(x\) belongs to a perforated domain \({\mathbb R}^n_\varepsilon\) included in \({\mathbb R}^n\), \(t\) belongs to \([0,T]\), and the coefficients \(a_{ij}\) are rapidly oscillating with period depending on \(\varepsilon\). The author constructs a complete asymptotic expansion for the Cauchy problem solution and obtains an estimate for the remainder term in this expansion.
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 1259427
zbMATH Keywords: rapidly oscillating coefficients
zbMATH Keywords: estimate for the remainder term
author: T. A. Shaposhnikova
reviewed by: Marco Codegone
MaRDI profile type: Publication
cites work: On the Convergence of the Energy, Stress Tensors, and Eigenvalues in Homogenization Problems of Elasticity
cites work: Q3746966
cites work: Q3948038
cites work: Q4189539
cites work: Homogenization in open sets with holes
cites work: Q4308736
description: scientific article; zbMATH DE number 1259427