Reaction-diffusion in irregular domains
type: Item
instance of: scholarly article
title: Reaction-diffusion in irregular domains
zbMATH Open document ID: 0956.35069
author: Ugur G. Abdulla
published in: Journal of Differential Equations
publication date: 2001-02-28T00:00:00Z
review text: The paper deals with the Cauchy-Dirichlet and Dirichlet problems for the reaction-diffusion equation which is a degenerate nonlinear parabolic one. The problems are considered in noncylindrical domains with nonsmooth boundaries. Under some restrictions existence, uniqueness and comparison theorems for generalized solutions are proved. The constructed solutions are continuous up to the nonsmooth boundary if at each interior point the left modulus of the lower (respectively upper) semicontinuity of the left (respectively right) boundary curve satisfies an upper (respectively lower) Hölder condition near zero with Hölder exponent \(\nu >1/2\).
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 1515446
zbMATH Keywords: Cauchy-Dirichlet problem
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: nonlinear degenerate parabolic equation
zbMATH Keywords: singular parabolic equation
zbMATH Keywords: noncylindrical domains
zbMATH Keywords: nonsmooth boundaries
zbMATH Keywords: boundary regularity
zbMATH Keywords: comparison theorems
reviewed by: G. Jaiani
MaRDI profile type: Publication
full work available at URL: jdeq.2000.3761
OpenAlex ID: W2047412529
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DOI: 10.1006/JDEQ.2000.3761
description: scientific article; zbMATH DE number 1515446