The Hölder property in some degenerate parabolic problems
type: Item
instance of: scholarly article
title: The Hölder property in some degenerate parabolic problems
zbMATH Open document ID: 0616.35041
DOI: 10.1016/0022-0396(86)90036-7
published in: Journal of Differential Equations
publication date: 1986-01-01T00:00:00Z
review text: The Hölder continuity of the degenerate parabolic equation \[ uu_{xx}+u^ 2_ x +h(x,t,u)u=u_ t \] with nonnegative initial data \(u_ 0(x)\) is demonstrated. In particular, it is shown that \(| u|_{\alpha}\leq K\), where K is independent of the modulus of continuity of h. A similar result is proved for the porous medium equation \(u_ t=(u^ m)_{xx}+h(x,t,u)u\).
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 76S05
zbMATH DE Number: 3998342
zbMATH Keywords: Hölder continuity
zbMATH Keywords: degenerate parabolic
zbMATH Keywords: nonnegative initial data
zbMATH Keywords: modulus of continuity
zbMATH Keywords: porous medium equation
author: Gaston E. Hernandez
reviewed by: S. P. Banks
MaRDI profile type: Publication
full work available at URL: 0022-0396(86)90036-7
OpenAlex ID: W2041906830
cites work: Regularity Propeties of Flows Through Porous Media
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description: scientific article; zbMATH DE number 3998342