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Mathematics and Mechanics of Solids
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Asymptotic Properties of Solutions to Nonlinear Possibly Degenerated Parabolic Equations in Unbounded Domains

S. Rionero

Dipartimento di Matematica ed Applicazioni "R. Caccioppoli", Università degli Studi di Napoli "Federico II", Via Cintia, Complesso Monte S. Angelo, 80126 Napoli, Italy

The nonlinear diffusion equation u t = {delta}F (u) is studied in exterior domains under Dirichlet boundary conditions. Asymptotic stability criteria for the steady states are proved. A criterion of pointwise asymptotic stability for the porous medium and horizontal filtration equations is obtained.

Key Words: PDEs • stability • porous media

Mathematics and Mechanics of Solids, Vol. 10, No. 5, 541-557 (2005)
DOI: 10.1177/1081286505036418
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