A nonlinear diffusion system coupled via nonlinear boundary flux

被引：0
|
作者：
Mi, Yongsheng [1 ,2 ]
Mu, Chunlai [1 ]
Chen, Botao [2 ]
机构：
[1] Chongqing Univ, Coll Math & Phys, Chongqing 400044, Peoples R China
[2] Yangtze Normal Univ, Coll Math & Comp Sci, Chongqing 408100, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2011年 / 376卷 / 02期
关键词：
Global existence curve; Nonlinear diffusion system; M-matrix; Nonlinear boundary flux; Blow-up; CRITICAL FUJITA EXPONENTS; POLYTROPIC FILTRATION EQUATION; DEGENERATE PARABOLIC-SYSTEM; HEAT-EQUATIONS; CRITICAL CURVES; COMPONENTS; THEOREMS;
D O I：
10.1016/j.jmaa.2010.10.065
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we deal with the global existence and nonexistence of solutions to a nonlinear diffusion system coupled via nonlinear boundary flux. By constructing various kinds of sub- and super-solutions and using the basic properties of M-matrix, we give the necessary and sufficient conditions for global existence of nonnegative solutions. The critical curve of Fujita type is conjectured with the aid of some new results, which extend the recent results of Wang et al. [Nonlinear Anal. 71 (2009) 2134-2140] and Li et al. U. Math. Anal. Appl. 340 (2008) 876-883] to more general equations. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：613 / 624
页数：12
相关论文
共 50 条
  • [1] GLOBAL EXISTENCE AND NONEXISTENCE FOR A DOUBLY DEGENERATE PARABOLIC SYSTEM COUPLED VIA NONLINEAR BOUNDARY FLUX
    Chen Botao
    Mi Yongsheng
    Mu Chunlai
    ACTA MATHEMATICA SCIENTIA, 2011, 31 (02) : 681 - 693
  • [2] CRITICAL EXPONENTS FOR A DOUBLY DEGENERATE PARABOLIC SYSTEM COUPLED VIA NONLINEAR BOUNDARY FLUX
    Mi, Yongsheng
    Mu, Chunlai
    Chen, Botao
    JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2011, 48 (03) : 513 - 527
  • [3] Critical curves for a fast diffusive polytropic filtration system coupled via nonlinear boundary flux
    Li, Zhongping
    Mu, Chunlai
    Cui, Zejian
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2009, 60 (02): : 284 - 298
  • [4] Global existence and nonexistence of the non-Newtonian polytropic filtration equations coupled with nonlinear boundary conditions
    Mi, Yongsheng
    Mu, Chunlai
    Li, Zhongping
    APPLICABLE ANALYSIS, 2010, 89 (12) : 1789 - 1803
  • [5] Critical curves for fast diffusion equations coupled via nonlinear boundary flux
    Ling, Zhengqiu
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2015,
  • [6] Critical exponents for porous medium systems coupled via nonlinear boundary flux
    Wang, Zejia
    Zhou, Qian
    Lou, Wenqi
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (5-6) : 2134 - 2140
  • [7] Critical parameter equations for degenerate parabolic equations coupled via nonlinear boundary flux
    Xu, Si
    Song, Zifen
    BOUNDARY VALUE PROBLEMS, 2011,
  • [8] Critical curves for a fast diffusive polytropic filtration system coupled via nonlinear boundary flux
    Zhongping Li
    Chunlai Mu
    Zejian Cui
    Zeitschrift für angewandte Mathematik und Physik, 2009, 60 : 284 - 298
  • [9] Blow-up estimates for system of heat equations coupled via nonlinear boundary flux
    Zhao, LZ
    Zheng, SN
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 54 (02) : 251 - 259
  • [10] Critical curves for fast diffusion equations coupled via nonlinear boundary flux
    Zhengqiu Ling
    Journal of Inequalities and Applications, 2015
12345