Local existence and lower bound of blow-up time to a Cauchy problem of a coupled nonlinear wave equations

被引：1
|
作者：
Kafini, Mohammad [1 ]
Al-Omari, Shadi [2 ]
机构：
[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, IR Ctr Construct & Bldg Mat, Dhahran 31261, Saudi Arabia
[2] King Fahd Univ Petr & Minerals, Dept Math, IR Ctr Construct & Bldg Mat, Preparatory Year Program, Dhahran 31261, Saudi Arabia
来源：
AIMS MATHEMATICS | 2021年 / 6卷 / 08期
关键词：
Cauchy problem; blow up; negative initial energy; nonlinear source; lower bound; GLOBAL NONEXISTENCE THEOREMS; EVOLUTION-EQUATIONS; INITIAL-ENERGY; UNIFORM DECAY; SYSTEM;
D O I：
10.3934/math.2021526
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider a Cauchy problem of a coupled linearly-damped wave equations with nonlinear sources. In the whole space, we establish the local existence and show that there are solutions with negative initial energy that blow up in a finite time. Moreover, under some conditions on the initial data, we estimate a lower bound of that time.
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页码：9059 / 9074
页数：16
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