Estimates of blow-up time for a non-local problem modelling an Ohmic heating process

Kavallaris, NI; Nikolopoulos, CV; Tzanetis, DE

dc.contributor.author	Kavallaris, NI	en
dc.contributor.author	Nikolopoulos, CV	en
dc.contributor.author	Tzanetis, DE	en
dc.date.accessioned	2014-03-01T01:17:49Z
dc.date.available	2014-03-01T01:17:49Z
dc.date.issued	2002	en
dc.identifier.issn	0956-7925	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14682
dc.subject	Blow Up	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	THERMISTOR PROBLEM	en
dc.subject.other	TEMPERATURE	en
dc.subject.other	EXISTENCE	en
dc.subject.other	EQUATIONS	en
dc.title	Estimates of blow-up time for a non-local problem modelling an Ohmic heating process	en
heal.type	journalArticle	en
heal.identifier.primary	10.1017/S0956792501004831	en
heal.identifier.secondary	http://dx.doi.org/10.1017/S0956792501004831	en
heal.language	English	en
heal.publicationDate	2002	en
heal.abstract	We consider an initial boundary value problem for the non-local equation, u(t) = u(xx) + lambdaf(u)/(integral(-1)(1)f (u)dx)(2), with Robin boundary conditions. It is known that there exists a critical value of the parameter lambda, say lambda, such that for lambda>lambda there is no stationary solution and the solution u(x,t) blows up globally in finite time t, while for lambda<λ there exist stationary solutions. We find, for decreasing f and for λ>lambda* upper and lower bounds for t, by using comparison methods. For f (u) = e(-u), we give an asymptotic estimate: t similar to t(u)(lambda-lambda)(-1/2) for 0<(λ-λ) &MLT; 1, where t(u) is a constant. A numerical estimate is obtained using a Crank-Nicolson scheme.	en
heal.publisher	CAMBRIDGE UNIV PRESS	en
heal.journalName	European Journal of Applied Mathematics	en
dc.identifier.doi	10.1017/S0956792501004831	en
dc.identifier.isi	ISI:000177267000005	en
dc.identifier.volume	13	en
dc.identifier.issue	3	en
dc.identifier.spage	337	en
dc.identifier.epage	351	en