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Global existence and asymptotic behaviour of solution for a damped nonlinear hyperbolic equation
Nonlinear Analysis ( IF 1.3 ) Pub Date : 2020-04-04 , DOI: 10.1016/j.na.2020.111885 Tiantian Pang , Jihong Shen
中文翻译:
阻尼非线性双曲型方程解的整体存在性和渐近性质
更新日期:2020-04-04
Nonlinear Analysis ( IF 1.3 ) Pub Date : 2020-04-04 , DOI: 10.1016/j.na.2020.111885 Tiantian Pang , Jihong Shen
In this paper we study the initial–boundary value problem for a damped nonlinear hyperbolic equation where , and is a positive constant. Under some assumptions on and initial data, we prove the global existence of solution. Furthermore, we prove that the solution decays to zero exponentially.
中文翻译:
阻尼非线性双曲型方程解的整体存在性和渐近性质
在本文中,我们研究了阻尼非线性双曲型方程的初边值问题 哪里 , 和 是一个正常数。根据一些假设和初始数据,我们证明了解决方案的全球存在。此外,我们证明了该解呈指数衰减至零。