Asymptotic Behavior of Solutions of the Porous Media Equation
Lambertus A. Peletier · SIAM Journal on Applied Mathematics · 1971
A degenerate quasi-linear parabolic equation which arises in the study of fluid flow through porous media is investigated. It is shown that the solutions of a class of mixed initial boundary value problems in the domain $x > 0$, $t > 0$ converge upon a suitably chosen similarity solution as $t \to \infty $. The rate of convergence is discussed.