Grow-up of critical solutions for a non-local porous medium problem with Ohmic heating source

Latos, EA; Tzanetis, DE

dc.contributor.author	Latos, EA	en
dc.contributor.author	Tzanetis, DE	en
dc.date.accessioned	2014-03-01T01:33:35Z
dc.date.available	2014-03-01T01:33:35Z
dc.date.issued	2010	en
dc.identifier.issn	1021-9722	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20470
dc.subject	Grow-up of solutions	en
dc.subject	Non-local parabolic problems	en
dc.subject	Porous medium	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	PARABOLIC PROBLEM	en
dc.title	Grow-up of critical solutions for a non-local porous medium problem with Ohmic heating source	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s00030-009-0044-7	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00030-009-0044-7	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	We investigate the behaviour of solution u = u( x, t; lambda) at lambda = lambda* for the non-local porous medium equation u(t) = (u(n))(xx) + lambda f( u)/(integral(1)(-1) f(u)dx)(2) with Dirichlet boundary conditions and positive initial data. The function f satisfies: f(s),- f'(s) > 0 for s >= 0 and s(n-1) f( s) is integrable at infinity. Due to the conditions on f, there exists a critical value of parameter lambda, say lambda, such that for lambda > lambda the solution u = u(x, t; lambda) blows up globally in finite time, while for lambda >= lambda* the corresponding steady-state problem does not have any solution. For 0 < lambda < lambda* there exists a unique steady-state solution w = w(x; lambda) while u = u(x, t; lambda) is global in time and converges to w as t -> infinity. Here we show the global grow-up of critical solution u* = u(x, t; lambda) (u( x, t) -> infinity, as t -> infinity for all x is an element of(- 1, 1)).	en
heal.publisher	BIRKHAUSER VERLAG AG	en
heal.journalName	Nonlinear Differential Equations and Applications	en
dc.identifier.doi	10.1007/s00030-009-0044-7	en
dc.identifier.isi	ISI:000276474000001	en
dc.identifier.volume	17	en
dc.identifier.issue	2	en
dc.identifier.spage	137	en
dc.identifier.epage	151	en