Blow-up of radially symmetric solutions of a non-local problem modelling Ohmic heating

Tzanetis, DE

dc.contributor.author	Tzanetis, DE	en
dc.date.accessioned	2014-03-01T01:17:35Z
dc.date.available	2014-03-01T01:17:35Z
dc.date.issued	2002	en
dc.identifier.issn	10726691	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14575
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dc.subject	Blow-up	en
dc.subject	Global existence	en
dc.subject	Nonlocal parabolic equations	en
dc.subject	Steady states	en
dc.title	Blow-up of radially symmetric solutions of a non-local problem modelling Ohmic heating	en
heal.type	journalArticle	en
heal.publicationDate	2002	en
heal.abstract	We consider a non-local initial boundary-value problem for the equation (Figure Presented) where u represents a temperature and / is a positive and decreasing function. It is shown that for the radially symmetric case, if f0∞ f(s) ds < ∝ then there exists a critical value λ* > 0 such that for λ > λ* there is no stationary solution and u blows up, whereas for λ < λ* there exists at least one stationary solution. Moreover, for the Dirichlet problem with - sf′(s) < f(s) there exists a unique stationary solution which is asymptotically stable. For the Robin problem, if λ < λ* then there are at least two solutions, while if λ = λ* at least one solution. Stability and blow-up of these solutions are examined in this article. © 2002 Southwest Texas State University.	en
heal.journalName	Electronic Journal of Differential Equations	en
dc.identifier.volume	2002	en
dc.identifier.spage	XXV	en
dc.identifier.epage	XXVI	en