Some interesting special cases of a non-local problem modelling ohmic heating with variable thermal conductivity

Tzanetis, DE; Vlamos, PM

dc.contributor.author	Tzanetis, DE	en
dc.contributor.author	Vlamos, PM	en
dc.date.accessioned	2014-03-01T01:17:07Z
dc.date.available	2014-03-01T01:17:07Z
dc.date.issued	2001	en
dc.identifier.issn	0013-0915	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14362
dc.subject	Blow-up	en
dc.subject	Local and global existence	en
dc.subject	Non-local parabolic equations	en
dc.subject	Stability	en
dc.subject	Stationary solutions	en
dc.subject.classification	Mathematics	en
dc.subject.other	THERMISTOR PROBLEM	en
dc.title	Some interesting special cases of a non-local problem modelling ohmic heating with variable thermal conductivity	en
heal.type	journalArticle	en
heal.identifier.primary	10.1017/S0013091500000109	en
heal.identifier.secondary	http://dx.doi.org/10.1017/S0013091500000109	en
heal.language	English	en
heal.publicationDate	2001	en
heal.abstract	The non-local equation u(t) = (u(3)u(x))x + lambdaf(u)/(integral (1/)(-1)f(u)dx)(2) is considered, subject to some initial and Dirichlet boundary conditions. Here f is taken to be either exp(-s(4)) or H(1 - s) with H the Heaviside function, which are both decreasing. It is found that there exists a critical value lambda* = 2, so that for lambda > lambda* there is no stationary solution and u 'blows up' (in some sense). If 0 < lambda < lambda*, there is a unique stationary solution which is asymptotically stable and the solution of the IBVP is global in time.	en
heal.publisher	CAMBRIDGE UNIV PRESS	en
heal.journalName	Proceedings of the Edinburgh Mathematical Society	en
dc.identifier.doi	10.1017/S0013091500000109	en
dc.identifier.isi	ISI:000171880300009	en
dc.identifier.volume	44	en
dc.identifier.issue	3	en
dc.identifier.spage	585	en
dc.identifier.epage	595	en