Non existence of global solutions of parabolic equation in conical domains
type: Item
instance of: scholarly article
title: Non existence of global solutions of parabolic equation in conical domains
zbMATH Open document ID: 0842.35044
author: Toshihiko Hamada
published in: Tsukuba Journal of Mathematics
publication date: 1995-12-20T00:00:00Z
review text: In this paper is studied the initial-boundary value problem \[ u_t = \Delta u + |x |^\sigma u^p \text{ in } D \times (0,T), \quad u(x,t) = 0 \text{ on } \partial D \times (0,T),\;u(x,0) - u_0 (x) \text{ in } D, \] where \(\sigma \geq 0\), \(p > 1\), \(u_0 \geq 0\), \((1 + |x |^2)^{\sigma/2 (p - 1)} u_0\) is continuous and bounded in \(\overline D\) and \(u_0 = 0\) on \(\partial D\). Two theorems about nonexistence of nontrivial global solutions are proved.
reviewed by: Josef Diblík
Mathematics Subject Classification ID: 35K60
zbMATH DE Number: 828336
zbMATH Keywords: conical domains
zbMATH Keywords: nonexistence of nontrivial global solutions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496162797
OpenAlex ID: W419106057
DOI: 10.21099/TKBJM/1496162797
description: scientific article; zbMATH DE number 828336