Logarithmic decay rate for a structural-acoustic interaction model with supercritical source and nonlinear damping

Haiyan Li; Victor R. Cabanillas; Donal O'Regan; Haiyan Li; Victor R. Cabanillas; Donal O'Regan

doi:10.3934/era.2026160

Electronic Research Archive

2026, Volume 34, Issue 5: 3573-3592. doi: 10.3934/era.2026160

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Research article

Logarithmic decay rate for a structural-acoustic interaction model with supercritical source and nonlinear damping

1.
College of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China
2.
Facultad de Ciencias Matemáticas - Universidad Nacional Mayor de San Marcos, Calle Germán Amézaga 375, Lima 15081, Perú
3.
School of Mathematical and Statistical Sciences, University of Galway, Galway, Ireland

Received: 08 February 2026 Revised: 28 March 2026 Accepted: 21 April 2026 Published: 27 April 2026

In this paper, we study a structural acoustics model with supercritical source and nonlinear damping. The model consists of a wave equation defined on a bounded domain which is strongly coupled with a Berger plate equation acting on the elastic wall. The aim of the paper is to remove the strong condition $ u\in L^\infty(\mathbb{R}^+; L^{\frac{3}{2}}(\Omega)) $ for $ m_1 > 5 $ in the work ^[1] to obtain a weaker energy decay, and give a logarithmic decay rate under a weak assumption on the initial data.
- structural acoustics model,
- energy decay,
- supercritical sources,
- nonlinear damping
Citation: Haiyan Li, Victor R. Cabanillas, Donal O'Regan. Logarithmic decay rate for a structural-acoustic interaction model with supercritical source and nonlinear damping[J]. Electronic Research Archive, 2026, 34(5): 3573-3592. doi: 10.3934/era.2026160

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Abstract

In this paper, we study a structural acoustics model with supercritical source and nonlinear damping. The model consists of a wave equation defined on a bounded domain which is strongly coupled with a Berger plate equation acting on the elastic wall. The aim of the paper is to remove the strong condition $ u\in L^\infty(\mathbb{R}^+; L^{\frac{3}{2}}(\Omega)) $ for $ m_1 > 5 $ in the work ^[1] to obtain a weaker energy decay, and give a logarithmic decay rate under a weak assumption on the initial data.

References

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