Existence and nonexistence of the global solution for the semilinear parabolic system on Riemannian manifold

被引：0
|
作者：
Ru, Qiang [1 ,2 ]
Duan, Zhi-wen [1 ]
机构：
[1] Huazhong Univ Sci & Technol, Dept Math, Wuhan 430074, Peoples R China
[2] Yang En Univ, Dept Math, Quanzhou 362014, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 72卷 / 02期
关键词：
Existence and nonexistence; Parabolic system; Riemannian manifolds; SCALAR CURVATURE; BLOW;
D O I：
10.1016/j.na.2009.07.042
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the global existence and nonexistence of solutions to the following semilinear parabolic system {u(t) - Delta u = v(p) in M-n x (0, infinity), v(t) - Delta v = u(p) in M-n x (0, infinity), u(x, 0) = u(0)(x) in M-n, v(x, 0) = v(0)(x) in M-n, where M-n (n >= 3) is a non-compact complete Riemannian manifold, Delta is the Laplace-Beltrami operator. We assume that both u(0)(x) and v(0)(x) are nonnegative, smooth and bounded functions, constants p, q >= 1. (C) 2009 Elsevier Ltd. All rights reserved.
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页码：856 / 866
页数：11
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