Nonlinear damped wave equation: Existence and blow-up

被引：77
作者：
Messaoudi, Salim A. [1 ]
Talahmeh, Ala A. [1 ]
Al-Smail, Jamal H. [1 ]
机构：
[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, POB 546, Dhahran 31261, Saudi Arabia
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2017年 / 74卷 / 12期
关键词：
Nonlinear damping; Blow up; Existence; Variable nonlinearity; GLOBAL NONEXISTENCE THEOREMS; VARIABLE EXPONENT; EVOLUTION-EQUATIONS; PARABOLIC EQUATIONS; SOBOLEV EMBEDDINGS; SPACES;
D O I：
10.1016/j.camwa.2017.07.048
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the following nonlinear wave equation with variable exponents: u(tt) - Delta u + au(t)vertical bar u(t)vertical bar(m(.)-2) = bu vertical bar u vertical bar(p(.)-2), where a, b are positive constants. By using the Faedo-Galerkin method, the existence of a unique weak solution is established under suitable assumptions on the variable exponents m and p. We also prove the finite time blow-up of solutions and give a two-dimension numerical example to illustrate the blow up result. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码：3024 / 3041
页数：18
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