### Instantaneous shrinking of the support in degenerate parabolic equations with strong absorption

Michael Winkler

#### Abstract

We investigate the phenomenon of instantaneous shrinking of the support of nonnegative solutions to the Cauchy problem in $\\mathbb R^n$ for $$u_t=f(u) \Delta u - g(u), \quad \mbox{where } f(0)=0.$$ Among other results, it is shown by means of comparison and integral techniques that under some structural assumptions on $f$ and $g$, a necessary {\em and} sufficient condition on the growth of $g$ near zero for instantaneous shrinking to occur is $\int_0^1 \frac{ds}{g(s)} <\infty$.

#### Article information

Source
Adv. Differential Equations, Volume 9, Number 5-6 (2004), 625-643.

Dates
First available in Project Euclid: 18 December 2012