Well-posedness and dynamics of wave equations with nonlinear damping and moving boundary

Qingquan Chang; Dandan Li

doi:10.3934/dcdsb.2024104

Article Contents

2025, Volume 30, Issue 2: 629-641. Doi: 10.3934/dcdsb.2024104

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Well-posedness and dynamics of wave equations with nonlinear damping and moving boundary

Qingquan Chang^1, , and
Dandan Li^{2, 3,}

1.
School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China
2.
Great Bay Institute for Advanced Study, Dongguan, 523000, China
3.
Great Bay University, Dongguan, 523000, China

^*Corresponding author: Qingquan Chang
^*Corresponding author: Qingquan Chang

Received: May 2024

Revised: July 2024

Early access: August 14, 2024

Published online: August 14, 2024

Qingquan Chang is supported by the National Natural Science Foundation of China Grant No.12201142, Dandan Li is supported by the National Natural Science Foundation of China Grant No.12301297.

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Abstract

We studied the longtime dynamical behavior of a wave equation with critical nonlinearity and nonlinear damping in an expanding domain. First, we employed the penalty approach to establish the local well-posedness of the weak solution. Subsequently, we illustrated energy dissipation and asymptotic compactness for both the penalized equations and the original equation. Lastly, we established the existence of pullback attractors for penalized equations and the original equation.

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Mathematics Subject Classification: Primary: 37L30; Secondary: 35B40, 35B41.

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