Journal
MONATSHEFTE FUR MATHEMATIK
Volume 142, Issue 1-2, Pages 81-111Publisher
SPRINGER WIEN
DOI: 10.1007/s00605-004-0237-4
Keywords
nonlinear parabolic equation; Porous Medium Equation; Dirichlet problem; asymptotic behavior
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The paper contains a complete study of the large-time behavior of solutions of the Porous Medium Equation, u(t) = Deltau(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.
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