The regularity of solutions of reaction-diffusion equations via Lagrangian coordinates
type: Item
instance of: scholarly article
title: The regularity of solutions of reaction-diffusion equations via Lagrangian coordinates
zbMATH Open document ID: 0861.35042
DOI: 10.1007/BF01193831
author: Sergei I. Shmarev
author: Juan Luis Vázquez
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 1997-05-04T00:00:00Z
review text: This article is concerned with the application of the method of Lagrangian coordinates to the reaction-diffusion equation \(u_t=(u^m)_{xx}+f(u)\), where \(m>1\) and \(f\) is a \(C^1\) function with \(f(0)=0\). The authors present a non-standard Lagrangian formulation that works in non-conservation cases and find the necessary estimates to prove the \(C^1\) regularity of moving interfaces and the regularity of the weak solution near such interfaces. The program succeeds for a quite general class of terms \(f(u)\), including all absorption terms of the form \(f(u)=-u^q\) with \(q\geq 1\) and reaction terms of the form \(f(u)=u^q\) if \(q\geq m\). The method can be applied to similar problems in several space dimensions with radial symmetry.
reviewed by: Vladimir N. Grebenev
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 952687
zbMATH Keywords: non-standard Lagrangian formulation
zbMATH Keywords: \(C^ 1\) regularity of moving interfaces
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01193831
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description: scientific article; zbMATH DE number 952687