Universal bounds for global solutions of a forced porous medium equation

We show that in a smooth bounded domain Omega subset of R-n, n greater than or equal to 2 all global nonnegative solutions of u(t) - Deltau(m) = u(p) with zero boundary data are uniformly bounded in Omega x (tau, infinity) by a constant depending on Omega, p and tau but not on u(0), provided that 1 < m < p < [(n + 1)/(n - 1)]m. Furthermore, we prove an a priori bound in L-infinity(Omega x (0, infinity)) depending on parallel tou(0)parallel to(Linfinity(Omega)) under the optimal condition 1 < m < p < [(n + 2)/(n - 2)]m. (C) 2004 Elsevier Ltd. All rights reserved.