Spatial Asymptotic Properties of a System Wave Equations with Nonlinear Damping and Source Terms

• 来源期刊: 数学季刊（英文版）
• 年，卷（期）: 2021,（1）
• 页码范围: 67-78
• 页数: 12页
• 分类号: O175.29
• 语种: 英文
• DOI: 10.13371/j.cnki.chin.q.j.m.2021.01.005

摘要

In this paper,the wave equation defined in a semi-infinite cylinder is considered,in which the nonlinear damping and source terms is included.By setting an arbitrary parameter greater than zero in the energy expression,the fast growth rate or decay rate of the solution with spatial variables is obtained by using energy analysis method and differential inequality technique.Secondly,we obtain the asymptotic behavior of the solution on the external domain of the sphere.In addition,in this paper we also give some useful remarks which show that our results can be extended to more models.