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arXiv · 2203.06312

Stability for nonlinear wave motions damped by time-dependent frictions

Zhe Jiao·Yong Xu·Lijing Zhao
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Abstract

We are concerned with the dynamical behavior of solutions to semilinear wave systems with time-varying damping and nonconvex force potential. Our result shows that the dynamical behavior of solution is asymptotically stable without any bifurcation and chaos. And it is a sharp condition on the damping coefficient for the solution to converge to some equilibrium. To illustrate our theoretical results, we provide some numerical simulations for dissipative sine-Gordon equation and dissipative Klein-Gordon equation.

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Zhe Jiao, Yong Xu, Lijing Zhao. 2022-03-12. Stability for nonlinear wave motions damped by time-dependent frictions. https://doi.org/10.1016/j.cnsns.2022.106965

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