RETRACTED ARTICLE: Decay estimates for the wave equation with partial boundary memory damping

Kun-Peng Jin; Can Liu; Kun-Peng Jin; Can Liu

doi:10.3934/nhm.2024060

Networks and Heterogeneous Media

2024, Volume 19, Issue 3: 1402-1423. doi: 10.3934/nhm.2024060

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Research article

RETRACTED ARTICLE: Decay estimates for the wave equation with partial boundary memory damping

Kun-Peng Jin ^{1,2
,
,},
Can Liu ¹

1.
Center for Applied Mathematics of Guangxi, Nanning Normal University, Nanning 530100, China
2.
Guangxi Key Lab of Human-machine Interaction and Intelligent Decision, Nanning Normal University, Nanning 530100, China
Retraction published on 27 December 2024, see NHM 2024, 19(4), 1470.

Received: 31 August 2024 Revised: 22 November 2024 Accepted: 29 November 2024 Published: 10 December 2024

In this paper, we discuss the wave equation with boundary memory damping. Notably, the system only involves the partial boundary memory damping, with no other types of damping (such as frictional damping) applied to the boundaries or the interior. Previous research on such boundary damping problems has focused on boundary friction damping terms or internal damping terms. By using the properties of positive definite kernels, high-order energy methods, and multiplier techniques, we demonstrate that the integrability of system energy is achieved if the kernel function is monotonically integrable, which indicates that the solution energy decays at a rate of at least $ t^{-1} $. This finding reveals that partial boundary memory damping alone is sufficient to generate a complete decay mechanism without additional, thereby improving upon related results.
- wave equations,
- boundary memory damping,
- positive definite kernels,
- stability,
- decay
Citation: Kun-Peng Jin, Can Liu. RETRACTED ARTICLE: Decay estimates for the wave equation with partial boundary memory damping[J]. Networks and Heterogeneous Media, 2024, 19(3): 1402-1423. doi: 10.3934/nhm.2024060

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Abstract

In this paper, we discuss the wave equation with boundary memory damping. Notably, the system only involves the partial boundary memory damping, with no other types of damping (such as frictional damping) applied to the boundaries or the interior. Previous research on such boundary damping problems has focused on boundary friction damping terms or internal damping terms. By using the properties of positive definite kernels, high-order energy methods, and multiplier techniques, we demonstrate that the integrability of system energy is achieved if the kernel function is monotonically integrable, which indicates that the solution energy decays at a rate of at least $ t^{-1} $. This finding reveals that partial boundary memory damping alone is sufficient to generate a complete decay mechanism without additional, thereby improving upon related results.

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