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.

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页码：2305 / 2336

页数：32

相关论文

共 35 条

[1] STABILIZATION OF SOLUTIONS OF A DEGENERATE NON-LINEAR DIFFUSION PROBLEM [J].

ARONSON, D ;

CRANDALL, MG ;

PELETIER, LA .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1982, 6 (10) :1001-1022

[2] THE CAUCHY-PROBLEM FOR THE NONLINEAR FILTRATION EQUATION IN AN INHOMOGENEOUS-MEDIUM [J].

EIDUS, D .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1990, 84 (02) :309-318

[3] THE FILTRATION EQUATION IN A CLASS OF FUNCTIONS DECREASING AT INFINITY [J].

EIDUS, D ;

KAMIN, S .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 120 (03) :825-830

[4]

FUJITA H, 1966, J FAC SCI U TOKYO 1, V13, P109

[5]

Galaktionov VA, 1997, COMMUN PUR APPL MATH, V50, P1

[6] Smoothing effects and infinite time blowup for reaction-diffusion equations: An approach via Sobolev and Poincare inequalities [J].

Grillo, Gabriele ;

Meglioli, Giulia ;

Punzo, Fabio .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2021, 151 :99-131

[7] Global existence of solutions and smoothing effects for classes of reaction-diffusion equations on manifolds [J].

Grillo, Gabriele ;

Meglioli, Giulia ;

Punzo, Fabio .

JOURNAL OF EVOLUTION EQUATIONS, 2021, 21 (02) :2339-2375

[8] POROUS MEDIA EQUATIONS WITH TWO WEIGHTS: SMOOTHING AND DECAY PROPERTIES OF ENERGY SOLUTIONS VIA POINCARE INEQUALITIES [J].

Grillo, Gabriele ;

Muratori, Matteo ;

Porzio, Maria Michaela .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2013, 33 (08) :3599-3640

[9] NONEXISTENCE OF GLOBAL SOLUTIONS OF SOME SEMILINEAR PARABOLIC DIFFERENTIAL EQUATIONS [J].

HAYAKAWA, K .

PROCEEDINGS OF THE JAPAN ACADEMY, 1973, 49 (07) :503-505

[10] An intrinsic metric approach to uniqueness of the positive Dirichlet problem for parabolic equations in cylinders [J].

Ishige, K .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 158 (02) :251-290

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