Asymptotic behaviour of the porous media equation in domains with holes
نویسندگان
چکیده
We study the asymptotic behaviour of solutions to the porous media equation in an exterior domain, Ω, which excludes one or several holes, with zero Dirichlet data on ∂Ω. We prove that, when the space dimension is three or more, this behaviour is given by a Barenblatt function away from the fixed boundary ∂Ω 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 ∂Ω. The height of such a function is determined by matching with the Barenblatt solution representing the outer behaviour.
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