Non-Negative Solutions of Generalized Porous Medium Equations

Abstract

The purpose of this paper is to study nonnegative solutions u of the nonlinear evolution equations ?u/?t = ?f(u), x I Rn, 0 < t < T = +8 (1.1) Here the nonlinearity f is assumed to be continuous, increasing with f(0) = 0. This equation arises in various physical problems, and specializing f leads to models for nonlinear filtrations, or for the gas flow in a porous medium. For a recent survey in these equations see [9]. The main object of this work is to study the initial value problem for (1,1).