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Existence and blow-up of solutions for a non-local filtration and porous medium problem

Part of: Parabolic equations and systems

Published online by Cambridge University Press:  12 January 2010

E. A. Latos  and
D. E. Tzanetis
E. A. Latos
Affiliation:
Department of Mathematics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece, Email: (dtzan@math.ntua.gr)
D. E. Tzanetis
Affiliation:
Department of Mathematics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece, Email: (dtzan@math.ntua.gr)
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Abstract

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We consider a non-local filtration equation of the form

and a porous medium equation, in this case K(u) = um, with some boundary and initial data u0, where 0 < p < 1 and f, f′, f″ > 0. We prove blow-up of solutions for sufficiently large values of the parameter λ > 0 and for any u0 > 0, or for sufficiently large values of u0 > 0 and for any λ λ 0.

Keywords

existenceblow-upnon-local parabolic problemsporous mediumfiltration equation

MSC classification

Secondary: 35K55: Nonlinear parabolic equations 35K60: Nonlinear initial value problems for linear parabolic equations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 1 , February 2010 , pp. 195 - 209
Copyright
Copyright © Edinburgh Mathematical Society 2010