一类双曲方程行波解的存在性及渐近稳定性

Journal of Jilin University Science Edition ›› 2022, Vol. 60 ›› Issue (5): 1064-1068.

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

SUN Cong¹, SONG Wenjing¹, YAN Dongze²

1. School of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China;
2. College of Mathematics, Jilin University, Changchun 130012, China

Received:2021-12-24 Online:2022-09-26 Published:2022-09-26

Abstract

Abstract: 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.

Key words: Klein-Gordon equation, mountain pass lemma, existence of , traveling wave solution, weighted , energy estimate, asymptotic , stability of , traveling wave solution

CLC Number:

SUN Cong, SONG Wenjing, YAN Dongze. Existence and Asymptotic Stability of Traveling Wave Solutions for a Class of Hyperbolic Equations[J].Journal of Jilin University Science Edition, 2022, 60(5): 1064-1068.

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

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