THE LIFESPAN OF SOLUTIONS FOR A VISCOELASTIC WAVE EQUATION WITH A STRONG DAMPING AND LOGARITHMIC NONLINEARITY

被引：6
|
作者：
Liao, Menglan [1 ,2 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China
[2] Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China
来源：
EVOLUTION EQUATIONS AND CONTROL THEORY | 2022年 / 11卷 / 03期
关键词：
Viscoelastic wave equations; blow-up; lifespan of solutions; strong damping; logarithmic nonlinearity; BLOW-UP; HYPERBOLIC EQUATION; GLOBAL SOLUTION; INSTABILITY;
D O I：
10.3934/eect.2021025
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper deals with the following viscoelastic wave equation with a strong damping and logarithmic nonlinearity: u(tt) - Delta u + integral(t)(0) g(t - s)Delta u(s)ds - Delta u(t) = vertical bar u vertical bar(p-2)u In vertical bar u vertical bar. A finite time blow-up result is proved for high initial energy. Meanwhile, the lifespan of the weak solution is discussed. The present results in this paper complement and improve the previous work that is obtained by Ha and Park.
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页码：781 / 792
页数：12
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