GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO THE POROUS MEDIUM EQUATION WITH REACTION AND SINGULAR COEFFICIENTS

被引：0

作者：

Meglioli, Giulia ^{[1
]}

机构：

[1] Univ Bielefeld, Fac Math, Bielefeld, Germany

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2023年 / 43卷 / 06期

关键词：

Porous medium equation; global existence; blow-up; sub-supersolutions; comparison principle; bounded domains; DEGENERATE PARABOLIC EQUATION; INTRINSIC METRIC APPROACH; NON-LINEAR DIFFUSION; LONG-TIME BEHAVIOR; CAUCHY-PROBLEM; INHOMOGENEOUS PME; FILTRATION EQUATION; BOUNDED SOLUTIONS; UNIQUENESS; NONUNIQUENESS;

D O I：

10.3934/dcds.2023011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study global in time existence versus blow-up in finite time of solutions to the Cauchy problem for the porous medium equation with a vari-able density rho(x) and a power-like reaction term posed in the one dimensional interval (-R, R), R > 0. Here the weight function is singular at the boundary of the domain (-R, R), indeed it is such that rho(x) (R - |x|)-q as |x|-+ R, with q > 0. We show a different behavior of solutions depending on the three cases when q > 2, q = 2 and q < 2.

引用

页码：2305 / 2336

页数：32

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