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The Dirichlet Problem for the Porous Medium Equation in Bounded Domains. Asymptotic Behavior
Authors:Juan Luis Vazquez
Affiliation:(1) Universidad Autónoma, Madrid, Spain
Abstract:
The paper contains a complete study of the large-time behavior of solutions of the Porous Medium Equation, ut = Deltaum with m > 1, posed in a bounded domain of the n-dimensional space with homogeneous boundary conditions. Asymptotic profiles are obtained and full proofs of the convergence results are given. Solutions with changing sign and problems posed in tubes are also considered.
Keywords:2000 Mathematics Subject Classification: 35K55   35K65   35K60   35B40
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