Differential and Integral Equations

Nonnegative weak solutions of a porous medium equation with strong absorption

Chung-Ki Cho

Abstract

This paper studies the nonnegative weak solutions of a porous medium equation with strong absorption. We prove an apriori $\text{L}^{\infty}$ estimate through Moser iteration and obtain a compactness theorem and an integral-type Harnack inequality. Using these fundamental results we prove the existence of initial traces of weak solutions and obtain the existence of a fundamental solution and the nonexistence of a very singular solution, as byproducts. As an another application of our apriori estimates we prove the finiteness of the propagation speed without using comparison principle

Article information

Source
Differential Integral Equations, Volume 11, Number 6 (1998), 847-874.

Dates
First available in Project Euclid: 30 April 2013