Dynamics of nonlinear parabolic systems with time delays
type: Item
instance of: scholarly article
title: Dynamics of nonlinear parabolic systems with time delays
zbMATH Open document ID: 0860.35138
author: C. V. Pao
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-07-18T00:00:00Z
review text: The authors consider the problem \[ u_t= \Delta u+ {\delta e^u \over \int_\Omega e^udx}, \quad (x,t) \in \Omega \times [0,T), \] \[ u(x,0) = u_0(x), \quad u(x,t) = 0,\;(x,t) \in \partial \Omega \times [0,T). \] This problem arises as a model for various interesting processes in engineering. The authors prove results on the steady state case, which are essentially the same as for the well known Gelfand problem (the problem without the integral in the denominator). They also prove existence results for the time dependent case.
reviewed by: René Sperb
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 906452
zbMATH Keywords: steady state case
zbMATH Keywords: Gelfand problem
zbMATH Keywords: existence
zbMATH Keywords: time dependent case
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0111
OpenAlex ID: W2055516191
DOI: 10.1006/JMAA.1996.0111
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description: scientific article; zbMATH DE number 906452