Stochastic quasilinear viscoelastic wave equation with nonlinear damping and source terms

被引：5
|
作者：
Kim, Sangil [1 ]
Park, Jong-Yeoul [2 ]
Kang, Yong Han [3 ]
机构：
[1] Hankuk Univ Foreign Studies, Yongin, South Korea
[2] Pusan Natl Univ, Dept Math, Busan, South Korea
[3] Catholic Univ Daegu, Inst Liberal Educ, Gyongsan, South Korea
来源：
BOUNDARY VALUE PROBLEMS | 2018年
基金：
新加坡国家研究基金会;
关键词：
stochastic quasilinear viscoelastic wave equation; blow-up of solution; global existence; BEAM EQUATION; BLOW-UP;
D O I：
10.1186/s13661-018-0932-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The goal of this study is to investigate an initial boundary value problem for the stochastic quasilinear viscoelastic wave equation involving the nonlinear damping vertical bar u(t)vertical bar(q-2)u(t) and a source term of the type vertical bar u vertical bar(p-2)u driven by additive noise. By an appropriate energy inequality, we prove that finite time blow-up is possible for equation (1.1) below if p > {q, p+2}and the initial data are large enough (that is, if the initial energy is sufficiently negative). Also, we show that if q >= p , the local solution can be extended for all time and is thus global.
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页数：15
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