COMPLEXITY OF ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE POROUS MEDIUM EQUATION WITH ABSORPTION

被引：0

作者：

尹景学 ^{[1
]}

王良伟 ^{[1
]}

黄锐 ^{[2
]}

机构：

[1] Department of Mathematics, Jilin University

[2] School of Mathematical Sciences, South China Normal University

来源：

Acta Mathematica Scientia | 2010年 / 30卷 / 06期

关键词：

complexity; asymptotic behavior; porous medium equation;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption u t-u m + γup = 0, where γ≥ 0, m > 1 and p > m + 2/N . We will show that if γ = 0 and 0 < μ < 2N/(N(m-1)+2), or γ > 0 and 1/(p-1)<μ<2N/(N(m-1)+2), then for any nonnegative function φ in a nonnegative countable subset F of the Schwartz space S (R N ), there exists an initial-value u0 ∈C(RN) with lim x →∞ u 0 (x) = 0 such that φ is an ω-limit point of the rescaled solutions t μ/2 u(t β·, t), where β =[2-μ(m-1)]/4 .

引用

页码：1865 / 1880

页数：16

共 50 条

[11] Asymptotic behavior for the critical nonhomogeneous porous medium equation in low dimensions [J].

Gabriel Iagar, Razvan ;

Sanchez, Ariel .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 439 (02) :843-863

[12] ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO COUPLED POROUS MEDIUM SYSTEMS WITH BOUNDARY DEGENERACY [J].

Zhao, Xutong ;

Zhou, Mingjun ;

Zhou, Qian .

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2022, 2022 (73)

[13] Proper spaces for the asymptotic convergence of solutions of porous medium equation [J].

Wang, Liangwei ;

Yin, Jingxue .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2017, 38 :261-270

[14] The Dirichlet problem for the porous medium equation in bounded domains. Asymptotic behavior [J].

Vazquez, JL .

NONLINEAR DIFFERENTIAL EQUATION MODELS, 2004, :81-111

[15] The Dirichlet problem for the Porous Medium Equation in bounded domains. Asymptotic behavior [J].

Vazquez, JL .

MONATSHEFTE FUR MATHEMATIK, 2004, 142 (1-2) :81-111

[16] ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO POROUS MEDIUM EQUATIONS WITH BOUNDARY DEGENERACY [J].

Zhao, Xutong ;

Zhou, Mingjun ;

Jing, Xinxin .

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2021,

[17] ON THE ASYMPTOTIC BEHAVIOUR OF SOLUTIONS TO THE FRACTIONAL POROUS MEDIUM EQUATION WITH VARIABLE DENSITY [J].

Grillo, Gabriele ;

Muratori, Matteo ;

Punzo, Fabio .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2015, 35 (12) :5927-5962

[18] Discrete solutions for the porous medium equation with absorption and variable exponents [J].

Almeida, Rui M. P. ;

Antontsev, Stanislav N. ;

Duque, Jose C. M. .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2017, 137 :109-129

[19] ASYMPTOTIC BEHAVIOUR OF A POROUS MEDIUM EQUATION WITH FRACTIONAL DIFFUSION [J].

Caffarelli, Luis A. ;

Luis Vazquez, Juan .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2011, 29 (04) :1393-1404

[20] Near Field Asymptotic Behavior for the Porous Medium Equation on the Half-Line [J].

Cortazar, Carmen ;

Quiros, Fernando ;

Wolanski, Noemi .

ADVANCED NONLINEAR STUDIES, 2017, 17 (02) :245-254

← 1 2 3 4 5 →