Stabilization of ill-posed Cauchy problems for parabolic equations
type: Item
instance of: scholarly article
title: Stabilization of ill-posed Cauchy problems for parabolic equations
zbMATH Open document ID: 0657.35065
DOI: 10.1007/BF01773944
author: Peter Knabner
author: Sergio Vessella
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1987-01-01T00:00:00Z
review text: We study the noncharacteristic Cauchy problem \(u_ t-(a(x)u_ x)_ x=0\), \(x\in (0,\ell)\), \(t\in (0,T]\), \(u(0,t)=\phi (t)\), \(u_ x(0,t)=0\), \(0\leq t\leq T\), assuming only \(L^{\infty}\) for a. In the case of weak a priori bounds on u, we derive stability estimates on u of Hölder type in the interior and of logarithmic type at the boundary. Also the continuous dependence on a is considered.
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35R25
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 4073564
zbMATH Keywords: noncharacteristic Cauchy problem
zbMATH Keywords: weak a priori bounds
zbMATH Keywords: stability estimates
zbMATH Keywords: Hölder type
zbMATH Keywords: logarithmic type
zbMATH Keywords: continuous dependence
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01773944
OpenAlex ID: W2068887394
description: scientific article; zbMATH DE number 4073564