Initial trace of solutions of some quasilinear parabolic equations with absorption
type: Item
instance of: scholarly article
title: Initial trace of solutions of some quasilinear parabolic equations with absorption
zbMATH Open document ID: 1010.35052
author: E. Chasseigne
author: Laurent Véron
author: Marie-Françoise Bidaut-Véron
published in: Journal of Functional Analysis
publication date: 2002-11-28T00:00:00Z
review text: There is studied the existence of an initial trace of nonnegative solutions of the equation \[ u_t-\nabla\big(|\nabla u|^{p-2}\nabla u\big)+ u^q=0 \;\;\text{in} \;\;Q_T=\Omega\times(0,T) \] with \(p>1, q>0\). There is proved that the initial trace is an outer regular Borel measure which may not be locally bounded for some values of the parameters \(p\) and \(q\). There is investigated also the solvability of the corresponding Cauchy problem with a given generalized Borel measure as initial data.
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1836675
zbMATH Keywords: \(p\)-Laplace
zbMATH Keywords: entropy solution
zbMATH Keywords: generalized measure
zbMATH Keywords: Borel measures
zbMATH Keywords: Cauchy problem with initial data measure
reviewed by: A. E. Shishkov
MaRDI profile type: Publication
OpenAlex ID: W2138200148
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DOI: 10.1006/JFAN.2002.3912
description: scientific article; zbMATH DE number 1836675