The asymptotic behaviour of solutions of a porous medium equation with bounded measurable coefficients
type: Item
instance of: scholarly article
title: The asymptotic behaviour of solutions of a porous medium equation with bounded measurable coefficients
zbMATH Open document ID: 0901.35045
author: Chung-Ki Cho
author: Hi Jun Choe
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-11-12T00:00:00Z
review text: In this interesting and well written paper the authors obtain the Hölder continuity of the interphases of (weak) solutions of \(u_t-\{a_{ij}(x) [u^m]_{x_i}\}_{x_j}=0 \) where \(x\in \mathbb{R}^n\), and the initial datum is assumed nonnegative, continuous and compactly supported. The matrix \([a_{ij}]\) is assumed to satisfy an ellipticity condition excluding degeneracy, having bounded and measurable coefficients. They also characterize the asymptotic behaviour of such solutions when \(t \to \infty\). The main tool is a very refined use of a weak Harnack inequality.
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1031646
zbMATH Keywords: free boundary problems
zbMATH Keywords: Hölder continuity of interphases
zbMATH Keywords: weak Harnack inequality
reviewed by: Marianne Korten
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5400
OpenAlex ID: W2085039655
cites work: Q3882115
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cites work: Source-type solutions of degenerate quasilinear parabolic equations
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cites work: Q5562267
DOI: 10.1006/JMAA.1997.5400
description: scientific article; zbMATH DE number 1031646