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.
Citation
V. A. Galaktionov. P. J. Harwin. "Spectra of critical exponents in nonlinear heat equations with absorption." Adv. Differential Equations 9 (3-4) 267 - 298, 2004. https://doi.org/10.57262/ade/1355867945
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