## 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