Asymptotic behaviour of the porous media equation in domains with holes | Zendy

Cristina Brändle | Zendy; Fernando Quirós | Zendy; Juan Luís Vázquez | Zendy

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Asymptotic behaviour of the porous media equation in domains with holes

Author(s) -

Cristina Brändle,

Fernando Quirós,

Juan Luís Vázquez

Publication year - 2007

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/162

Subject(s) - mathematical analysis , boundary (topology) , domain (mathematical analysis) , porous medium , mathematics , harmonic function , function (biology) , dimension (graph theory) , dirichlet boundary condition , space (punctuation) , boundary value problem , zero (linguistics) , porosity , pure mathematics , materials science , linguistics , philosophy , evolutionary biology , composite material , biology

We study the asymptotic behaviour of solutions to the porous media equation in an exterior domain, ›, which excludes one or several holes, with zero Dirichlet data on @›. We prove that, when the space dimension is three or more, this behaviour is given by a Barenblatt function away from the flxed boundary @› and near the free-boundary. On the other hand, if we scale the solution according to its decay factor, away from the free boundary and close to the holes it behaves like a function whose m-th power, H, is harmonic and vanishes at @›. The height of such a function is determined by matching with the Barenblatt solution representing the outer behaviour.

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