Global existence and asymptotic behaviour of solution for a damped nonlinear hyperbolic equation

被引：2
|
作者：
Pang, Tiantian [1 ]
Shen, Jihong [1 ]
机构：
[1] Harbin Engn Univ, Coll Math Sci, Harbin 150001, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2020年 / 198卷
关键词：
ENERGY;
D O I：
10.1016/j.na.2020.111885
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study the initial–boundary value problem for a damped nonlinear hyperbolic equation utt+Δ2u+αΔ2ut+Δf(Δu)=0,x∈Ω,t>0,u(x,0)=u0(x),ut(x,0)=u1(x),x∈Ω,u=0Δu=0,x∈∂Ω,t≥0, where Ω⊂Rn, n≥1 and α is a positive constant. Under some assumptions on f(s) and initial data, we prove the global existence of solution. Furthermore, we prove that the solution decays to zero exponentially. © 2020 Elsevier Ltd
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