On the attractor for a semilinear wave equation with variable coefficients and nonlinear boundary dissipation

Jiacheng Wang; Peng-Fei Yao

doi:10.3934/cpaa.2021043

Article Contents

2022, Volume 21, Issue 6: 1857-1871. Doi: 10.3934/cpaa.2021043

This issue Previous Article Next Article Stabilized finite element methods based on multiscale enrichment for Allen-Cahn and Cahn-Hilliard equations

On the attractor for a semilinear wave equation with variable coefficients and nonlinear boundary dissipation

Jiacheng Wang^1,2, and
Peng-Fei Yao^1,2, ,

1.
Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
2.
School of Mathematical Sciences University of Chinese Academy of Sciences, Beijing 100049, China

^* Corresponding author
^* Corresponding author

Received: October 2020

Revised: January 2021

Published: June 2022

The work is supported by the National Science Foundation of China, grants no. 12071463 and no. 61573342 and Key Research Program of Frontier Sciences, CAS, no. QYZDJ-SSW-SYS011

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Abstract

Long time behavior of a semilinear wave equation with variable coefficients with nonlinear boundary dissipation is considered. It is shown that the existence of global and compact attractors depends on the curvature properties of a Riemannian metric given by the variable coefficients.

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Mathematics Subject Classification: Primary: 93C20, 93D20.

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References

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