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Monatshefte für Mathematik

, Volume 142, Issue 1–2, pp 81–111 | Cite as

The Dirichlet Problem for the Porous Medium Equation in Bounded Domains. Asymptotic Behavior

  • Juan Luis Vazquez
Article

Abstract.

The paper contains a complete study of the large-time behavior of solutions of the Porous Medium Equation, u t = Δu m 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.

2000 Mathematics Subject Classification: 35K55, 35K65, 35K60, 35B40 
Key words: Nonlinear parabolic equation, porous medium equation, Dirichlet problem, asymptotic behavior 

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Copyright information

© Springer-Verlag/Wien 2004

Authors and Affiliations

  • Juan Luis Vazquez
    • 1
  1. 1.Universidad AutónomaMadridSpain

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