Critical extinction exponents for a polytropic filtration equation with absorption and source

Abstract

In this paper, instead of energy methods, we apply the supersolution and subsolution methods to investigate the critical extinction exponents for a polytropic filtration equation with absorption and source, and improve the results of Mu et al. (J. Math. Anal. Appl. 2012; 391:429–440). Copyright © 2012 John Wiley & Sons, Ltd.

Extinction behavior of solutions for a quasilinear parabolic system with nonlocal sources

“…Recently, many authors have studied the extinction properties of solutions to nonlinear parabolic equations with the local (or nonlocal) source and absorption (see [10,22,29,32] and the references therein). For example, Liu [21] studied the extinction properties of solutions to the following problem with the nonlocal source and absorption where q; p 2 ð0; 1Þ; d; k > 0; X & R N (N P 2), and obtained the critical extinction exponent q ¼ p.…”

Extinction Phenomenon and Decay Estimate for a Quasilinear Parabolic Equation with a Nonlinear Source

“…Extinction phenomenon, as one of the most remarkable properties that distinguish nonlinear parabolic problems from the linear ones, attracted extensive attentions of mathematicians in the past few decades (see [5][6][7][8][9][10][11][12][13][14][15][16] and the references therein). Especially, many authors devoted to concern with the extinction behavior of the following parabolic problem…”

Global Existence and Extinction Singularity for a Fast Diffusive Polytropic Filtration Equation with Variable Coefficient

“…subject to various assumptions (see [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and the references therein). For the case s � 0, the authors in [24][25][26] concerned with the global existence and blow-up properties of the solutions to problem (4) with m � 1 and p ≥ 2.…”