Advances in Differential Equations

Spectra of critical exponents in nonlinear heat equations with absorption

V. A. Galaktionov and P. J. Harwin

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 18 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B33: Critical exponents 35B40: Asymptotic behavior of solutions 47N20: Applications to differential and integral equations


Galaktionov, V. A.; Harwin, P. J. Spectra of critical exponents in nonlinear heat equations with absorption. Adv. Differential Equations 9 (2004), no. 3-4, 267--298.

Export citation