LOCAL AND GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO A POLYTROPIC FILTRATION SYSTEM WITH NONLINEAR MEMORY AND NONLINEAR BOUNDARY CONDITIONS

被引：0

作者：

Wang, Jian ^{[1
]}

Su, Meng-Long ^{[2
]}

Fang, Zhong-Bo ^{[1
]}

机构：

[1] Ocean Univ China, Dept Math, Qingdao 266100, Peoples R China

[2] Luoyang Normal Univ, Coll Math, Luoyang 471022, Peoples R China

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2013年 / 50卷 / 01期

关键词：

nonlinear boundary value problem; nonlinear memory; polytropic filtration system; global existence; blow-up; REACTION-DIFFUSION SYSTEM; DEGENERATE; EQUATIONS;

D O I：

10.4134/BKMS.2013.50.1.037

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with the behavior of positive solutions to the following nonlocal polytropic filtration system [GRAPHICS] with nonlinear boundary conditions u(x)vertical bar(x=a) = u(q11)v(q12)vertical bar(x=a), v(x)vertical bar(x=0) = 0, v(x)vertical bar(x=a) = u(q21)v(q22)vertical bar(x=a) and the initial data (u(0), v(0)), where m(1), m(2) > 1, P-1,P-2 > 1, l(11), l(12), l(21), l(22), q(11), q(12), q(21), q(22) > 0. Under appropriate hypotheses, the authors establish local theory of the solutions by a regularization method and prove that the solution either exists globally or blows up in finite time by using a comparison principle.

引用

页码：37 / 56

页数：20

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