Asymptotic analysis and estimates of blow-up time for the radial symmetric semilinear heat equation in the open-spectrum case

Kavallaris, NI; Lacey, AA; Nikolopoulos, CV; Tzanetis, DE

dc.contributor.author	Kavallaris, NI	en
dc.contributor.author	Lacey, AA	en
dc.contributor.author	Nikolopoulos, CV	en
dc.contributor.author	Tzanetis, DE	en
dc.date.accessioned	2014-03-01T01:25:57Z
dc.date.available	2014-03-01T01:25:57Z
dc.date.issued	2007	en
dc.identifier.issn	0170-4214	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17843
dc.subject	Blow-up time estimates	en
dc.subject	Boundary-layer theory	en
dc.subject	Reaction diffusion equation	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Asymptotic analysis	en
dc.subject.other	Computer simulation	en
dc.subject.other	Function evaluation	en
dc.subject.other	Linear equations	en
dc.subject.other	Numerical methods	en
dc.subject.other	Blow-up time estimates	en
dc.subject.other	Boundary-layer theory	en
dc.subject.other	Diffusion equation	en
dc.subject.other	Reaction diffusion equation	en
dc.subject.other	Equations of state	en
dc.title	Asymptotic analysis and estimates of blow-up time for the radial symmetric semilinear heat equation in the open-spectrum case	en
heal.type	journalArticle	en
heal.identifier.primary	10.1002/mma.854	en
heal.identifier.secondary	http://dx.doi.org/10.1002/mma.854	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	We estimate the blow-up time for the reaction diffusion equation u(t) = Delta u + lambda f (u), for the radial symmetric case, where f is a positive, increasing and convex function growing fast enough at infinity. Here lambda >lambda, where lambda is the 'extremal' (critical) value for lambda, such that there exists an 'extremal' weak but not a classical steady-state solution at lambda=lambda* with parallel to w(., lambda)parallel to(infinity)->infinity as 0 <lambda ->lambda-. Estimates of the blow-up time are obtained by using comparison methods. Also an asymptotic analysis is applied when f (s) = e(s), for lambda-lambda << 1, regarding the form of the solution during blow-up and an asymptotic estimate of blow-up time is obtained. Finally, some numerical results are also presented. Copyright (c) 2007 John Wiley & Sons, Ltd.	en
heal.publisher	JOHN WILEY & SONS LTD	en
heal.journalName	Mathematical Methods in the Applied Sciences	en
dc.identifier.doi	10.1002/mma.854	en
dc.identifier.isi	ISI:000248554900002	en
dc.identifier.volume	30	en
dc.identifier.issue	13	en
dc.identifier.spage	1507	en
dc.identifier.epage	1526	en