### Spectra of critical exponents in nonlinear heat equations with absorption

#### Abstract

It has been known from the beginning of the 1980's that the global $L^1$ solutions of the classical porous medium equation with absorption $u_t = \Delta u^m - u^p$ in $\mathbb R^N \times \mathbb R_+$, with $m,p>1$ change their large-time behavior at the critical absorption exponent $p_0=m+2/N$. We show that, actually, there exists an infinite sequence $\{p_k, \, k \ge 0\}$ of critical exponents generating a countable subset of different non-self-similar asymptotic patterns. The results are extended to the fully nonlinear dual porous-medium equation with absorption.

#### Article information

Source
Adv. Differential Equations, Volume 9, Number 3-4 (2004), 267-298.

Dates
First available in Project Euclid: 18 December 2012