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

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