Smooth solution for the porous medium equation in a bounded domain
type: Item
instance of: scholarly article
title: Smooth solution for the porous medium equation in a bounded domain
zbMATH Open document ID: 1180.35308
author: Ki-Ahm Lee
author: Sung Hoon Kim
published in: Journal of Differential Equations
publication date: 2009-07-09T00:00:00Z
review text: There is considered the problem with unknown function (1) \(u(x,t): u_t=\Delta u^m\) in \(\Omega\subset \mathbb{R}^n\), \(u|_{t=0}=u_0\) in \(\Omega\), \(u_{\partial \Omega}=0\), where \(m>1\), \(u_0\) is nonnegative and compactly supported in \(\Omega\) function. After the substitution \(f=u^m\) the problem (1) is reduced to the problem, for which the short time existence of the solution \(f\) in the weighted Hölder space is established. To prove this the authors obtain solvability and coercive estimate of the solution of a corresponding model linearized problem in \(\mathbb{R}^n_+\) for the equation \(f_t-x_n^\alpha \Delta f=g\), \(\alpha\in(0,1)\).
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K59
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 5577109
zbMATH Keywords: existence
zbMATH Keywords: weighted Hölder space
zbMATH Keywords: coercive estimate
reviewed by: Galina Bizhanova
MaRDI profile type: Publication
full work available at URL: j.jde.2009.05.001
OpenAlex ID: W2061383526
Wikidata QID: Q125291637
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DOI: 10.1016/J.JDE.2009.05.001
description: scientific article; zbMATH DE number 5577109