A note on nonexistence of global solutions to a nonlinear integral equation
type: Item
instance of: scholarly article
title: A note on nonexistence of global solutions to a nonlinear integral equation
zbMATH Open document ID: 0953.45006
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2001-01-25T00:00:00Z
review text: The authors consider the equation \(u_t=-(-\Delta)^{\beta/2} u+h(t)u^{1+ \alpha}\) in \(\mathbb{R}^n \times (0,T)\), where \(0<\beta\leq 2\). They extend results of \textit{H. Fujita}, who treated the case \(\beta=2\) and \(h\equiv 1\) [J. Fac. Sci., Univ. Tokyo, Sect. I 13, 109-124 (1966; Zbl 0163.34002)]. The main result of the present paper gives sufficient conditions so that a solution \(u\) of the considered equation blows up in finite time, that means there exists \(T_0\) so that \(u(x,t)=\infty\) for every \(t\geq T_0\) and \(x\in \mathbb{R}^n\).
reviewed by: Marianne Reichert
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 1421340
zbMATH Keywords: nonexistence of global solutions
zbMATH Keywords: nonlinear integral equation
zbMATH Keywords: blow up of solutions
author: M. Guedda
author: Mokhtar Kirane
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1421340