Cauchy problem of some doubly degenerate parabolic equations with initial datum a measure
type: Item
instance of: scholarly article
title: Cauchy problem of some doubly degenerate parabolic equations with initial datum a measure
zbMATH Open document ID: 1073.35130
author: Huijun Fan
publication date: 2005-01-25T00:00:00Z
review text: The author studies the existence of nonnegative solutions of the Cauchy problem \(u_t=\nabla\cdot(| \nabla u^m| ^{p-2}\nabla u^m)-u^q\) in \(\mathbb R^N\times(0,\infty)\), \(u(\cdot,0)=\mu\) in \(\mathbb R^N\), where \(p>1\), \(m>0\), \(q>0\) and \(\mu\) is a nonnegative bounded Radon measure. The existence is proved provided \(m(p-1)+p/N>1\) and \(q<m(p-1)+p/N\). It is also shown that these conditions are essentially optimal. The existence proof is based on the approximation of \(\mu\) by smooth functions.
reviewed by: Pavol Quittner
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 2130973
zbMATH Keywords: degenerate parabolic equation
zbMATH Keywords: measure data
zbMATH Keywords: Cauchy problem
zbMATH Keywords: nonnegative bounded Radon measure
MaRDI profile type: Publication
full work available at URL: s10114-004-0375-6
OpenAlex ID: W2016611786
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DOI: 10.1007/S10114-004-0375-6
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 2130973