一类双曲方程行波解的存在性及渐近稳定性  

Existence and Asymptotic Stability of Traveling Wave Solutions for a Class of Hyperbolic Equations

作　　者：孙聪 宋文晶[1] 闫东泽 SUN Cong;SONG Wenjing;YAN Dongze(School of Applied Mathematics,Jilin University of Finance and Economics,Changchun 130117,China;College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[1]吉林财经大学应用数学学院,长春130117 [2]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2022年第5期1064-1068,共5页Journal of Jilin University:Science Edition

基　　金：吉林省教育厅“十四五”科学技术研究规划项目(批准号:JJKH20210130KJ)。

摘　　要：首先,采用山路引理证明具有复杂非线性源项的Klein-Gordon方程行波解的存在性;其次,在初值条件下使用扰动函数法和加权能量估计法,证明该方程的行波解具有渐近稳定性.Firstly, we proved the existence of traveling wave solutions for Klein-Gordon equations with complex nonlinear source terms by using the mountain pass lemma. Secondly, we proved that the traveling wave solution of the equation had asymptotic stability by using the perturbation function method and the weighted energy estimate method under the initial conditions.

关 键 词：KLEIN-GORDON方程 山路引理 行波解的存在性 加权的能量估计 行波解的渐近稳定性 

分 类 号：O175.27[理学—数学]