Asymptotic behaviour and blow-up of some unbounded solutions for a semilinear heat equation

Tzanetis, DE

dc.contributor.author	Tzanetis, DE	en
dc.date.accessioned	2014-03-01T01:11:45Z
dc.date.available	2014-03-01T01:11:45Z
dc.date.issued	1996	en
dc.identifier.issn	0013-0915	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/11794
dc.subject	Asymptotic Behaviour	en
dc.subject	Blow Up	en
dc.subject	semilinear heat equation	en
dc.subject.classification	Mathematics	en
dc.subject.other	PARABOLIC EQUATIONS	en
dc.subject.other	POSITIVE SOLUTIONS	en
dc.title	Asymptotic behaviour and blow-up of some unbounded solutions for a semilinear heat equation	en
heal.type	journalArticle	en
heal.identifier.primary	10.1017/S001309150002280X	en
heal.identifier.secondary	http://dx.doi.org/10.1017/S001309150002280X	en
heal.language	English	en
heal.publicationDate	1996	en
heal.abstract	The initial-boundary value problem for the nonlinear heat equation u(t)=Delta u+lambda f(u) might possibly have global classical unbounded solutions, u=u(x,t;u(0)), for some ''critical'' initial data u(0). The asymptotic behaviour of such solutions is studied, when there exists a unique bounded steady state w(x;lambda) for some values of lambda. We find, for radial symmetric solutions, that u(r,t)-->w(r) for any 0<r less than or equal to 1 but supu(.,t)=u(0,t)-->infinity, as t-->infinity. Furthermore, if (u) over cap(0)>u(0), where u(0) is some such critical initial data, then (u) over cap=u(x,t;(u) over cap(0)*) blows up in finite time provided that f grows sufficiently fast.	en
heal.publisher	OXFORD UNIV PRESS UNITED KINGDOM	en
heal.journalName	Proceedings of the Edinburgh Mathematical Society	en
dc.identifier.doi	10.1017/S001309150002280X	en
dc.identifier.isi	ISI:A1996TY50600009	en
dc.identifier.volume	39	en
dc.identifier.issue	1	en
dc.identifier.spage	81	en
dc.identifier.epage	96	en