Rate of convergence to a singular steady state of a supercritical parabolic equation
type: Item
instance of: scholarly article
title: Rate of convergence to a singular steady state of a supercritical parabolic equation
zbMATH Open document ID: 1175.35071
author: Marek Fila
author: Michael Winkler
published in: Journal of Evolution Equations
publication date: 2009-06-08T00:00:00Z
review text: The authors study global positive solutions to the Cauchy problem for a supercritical parabolic equation of the type \[ \begin{cases} u_t=\Delta u+ u^p & x\in \mathbb R^N,\;t>0,\\ u(x,0)=u_0(x) & x\in \mathbb R^N, \end{cases} \] which converge to a steady state that is singular at \(x=0\). Here \(u_0\) is a nonnegative continuous function in \(\mathbb R^N\) and the exponent \(p\) is greater than the critical value \[ {{(N-2)^2-4N+8\sqrt{N-1}}\over {(N-2)(N-10)}},\quad N>10. \] The rate of convergence to the singular steady state is determined in \(L^\infty({\mathbb{R}}^{N} \setminus B_{\nu}(0))\) where \(B_\nu(0)\) is an \(N\)-dimensional ball centered at the origin and of radius \(\nu\).
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35B33
zbMATH DE Number: 5562657
zbMATH Keywords: semilinear parabolic equation
zbMATH Keywords: global positive solutions
MaRDI profile type: Publication
full work available at URL: s00028-008-0400-9
OpenAlex ID: W1969118570
DOI: 10.1007/S00028-008-0400-9
description: scientific article; zbMATH DE number 5562657