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Stability of Wave Equation with Variable Coefficients by Boundary Fractional Dissipation Law

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Abstract

In this paper, we consider the boundary stability of the wave equation with variable coefficients and fractional dam** acting on part of the boundary. The acceleration terms on the boundary are involved as well. It has been known that the presence of such dynamic structures on the boundary may change drastically the stability property of the underlying system. We obtain the polynomial decay for the solutions by applying a boundary fractional dissipation law. Our proof relies on the geometric multiplier skill and frequency domain method.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Hui Ge & Zhifei Zhang

  2. Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China

    Hui Ge & Zhifei Zhang

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  1. Hui Ge
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  2. Zhifei Zhang
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All authors contributed to the study conception. Material preparation and analysis were performed by HG and ZZ. We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work.

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Correspondence to Zhifei Zhang.

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This work is supported by the National Science Foundation of China under Grant 61473126 and by the Fundamental Research Funds for the Central Universities.

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Ge, H., Zhang, Z. Stability of Wave Equation with Variable Coefficients by Boundary Fractional Dissipation Law. Results Math 79, 64 (2024). https://doi.org/10.1007/s00025-023-02096-x

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