Stabilization of Flows Through Porous Media
Brian H. Gilding · SIAM Journal on Mathematical Analysis · 1979
Let $u(x,t)$ be the solution of the Cauchy–Dirichlet problem for the porous media equation in one space dimension in the quarter-plane $(0,\infty ) \times (0,\infty )$. An estimate is obtained for the asymptotic behaviour of $u(t,x)$ as $t \to \infty $, in terms of the prescribed lateral boundary value of u. The paper is an enlargement on a result of Peletier [SIAM J. Appl. Math, 1971].