Second critical exponent and life span for pseudo-parabolic equation
type: Item
instance of: scholarly article
title: Second critical exponent and life span for pseudo-parabolic equation
zbMATH Open document ID: 1278.35140
author: Chunxiao Yang
author: Yang Cao
author: Sining Zheng
published in: Journal of Differential Equations
publication date: 2012-11-22T00:00:00Z
review text: The authors study the second critical exponent and the life span for the equation \[ u_t-k\Delta u_t=\Delta u+u^p\quad (x,t)\in{\mathbb R}^n\times(0,T) \] with initial condition \(u(x,0)=u_0(x)\) and parameters \(p>1\) and \(k>0\). They consider the problem in an equivalent form as nonlocal diffusion equation instead of the standard energy estimates method. It is proved that the decay order of the initial data required by global solutions in the coexisting region of global and non-global solutions depends on the pseudo-parabolic parameter \(k\). In the last part, the authors give some numerical examples to illustrate all obtained results.
Mathematics Subject Classification ID: 35K70
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35B44
zbMATH DE Number: 6109960
zbMATH Keywords: pseudo-parabolic equation
zbMATH Keywords: second critical exponent
zbMATH Keywords: life span
reviewed by: Georgiĭ Anatol'evich Sviridyuk
MaRDI profile type: Publication
full work available at URL: j.jde.2012.09.001
OpenAlex ID: W2075977491
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DOI: 10.1016/J.JDE.2012.09.001
description: scientific article; zbMATH DE number 6109960