Global nonexistence for the Cauchy problem of some nonlinear reaction-diffusion systems
type: Item
instance of: scholarly article
title: Global nonexistence for the Cauchy problem of some nonlinear reaction-diffusion systems
zbMATH Open document ID: 1006.35011
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-07-04T00:00:00Z
review text: This paper is devoted to a series of problems concerning critical exponents for some nonlinear reaction-diffusion equations. They start by considering the nonautonomous diffusive-convective parabolic equation with a fractal diffusion \[ u_t=- (-\Delta)^{\alpha/2} u^m+a(x)\cdot\nabla u^q+f (t,x)|u|^p+ w(t,x), \tag{\(E_m\)} \] for \(t>0\), \(x\in\mathbb{R}^N\), supplemented with the initial condition \(u(0,x)=u_0(x)\), \(x\in\mathbb{R}^N\), where \(m,p,\) and \(q\) are positive reals. The authors find conditions relating the space dimension \(N\) with the parameters \(\alpha,m,q\), and \(p\) for which every global nontrivial solution of \((E_m)\) is trivial. The results of the authors answer positively some open problems raised recently by Bandle, Dengs, Levine, and Zhang.
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 1763454
zbMATH Keywords: fractal diffusion
author: Mokhtar Kirane
author: Mahmoud Qafsaoui
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: jmaa.2001.7819
OpenAlex ID: W2070948652
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DOI: 10.1006/JMAA.2001.7819
description: scientific article; zbMATH DE number 1763454