Standing waves and global existence for nonlinear wave equations with potential, strong, and nonlinear damping terms

Boundary value problems

Wenyi Huang¹ 

[1] Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu, China

关键词: wave equations;    nonlinear damping terms;    strong damping terms;    global existence;    blow-up;   

DOI  :  10.1186/s13661-014-0144-0

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper is concerned with the Cauchy problem of nonlinear wave equations with potential, strong, and nonlinear damping terms. Firstly, by using variational calculus and compactness lemma, the existence of standing waves of the ground states is obtained. Then the instability of the standing wave is shown by applying potential-well arguments and concavity methods. Finally, we show how small the initial data are for the global solutions to exist.

【 授权许可】

CC BY