Convergence to self-similar solutions for a semilinear parabolic equation
type: Item
instance of: scholarly article
title: Convergence to self-similar solutions for a semilinear parabolic equation
zbMATH Open document ID: 1155.35005
author: Marek Fila
author: Michael Winkler
author: Eiji Yanagida
published in: Discrete and Continuous Dynamical Systems
publication date: 2008-07-29T00:00:00Z
review text: The authors consider the following Cauchy problem \[ u_t=\Delta u+u^p,\quad x\in \mathbb{R}^N,\;t>0, \qquad u( x,0) =u_0( x) ,\quad x\in \mathbb{R}^N, \] where \(u_0\) is a nonnegative continuous function on \(\mathbb R^N\). Considering solutions which converge to self-similar solutions as \(t\to \infty\), the authors concern is the rate of convergence depending on the behavior of initial data. More precisely, given a specific decay rate of \(u_0\) as \(| x| \to \infty\), the authors determine the exact rate of the convergence. The article presented is a part of a research project on quantitative description of the behavior of solutions. So far, the authors have determined in previous articles the grow-up decay of solutions, the convergence rate to regular steady states and the decay rate to the trivial solution.
reviewed by: Cristian Chifu
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 5304861
zbMATH Keywords: comparison principle
MaRDI profile type: Publication
full work available at URL: dcds.2008.21.703
OpenAlex ID: W2331309937
DOI: 10.3934/DCDS.2008.21.703
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description: scientific article; zbMATH DE number 5304861