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

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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

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