Asymptotic Properties of Solutions to Nonlinear Possibly Degenerated Parabolic Equations in Unbounded Domains

Abstract

The nonlinear diffusion equation u _t = δF (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.

Keywords

PDEs stability porous media

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