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General Decay for Semi-Linear Wave Equations with Memory Term and Logarithmic Source

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Abstract

In this work we investigate asymptotic stability of solutions for logarithmic wave equations. Some assumptions on the memory kernel g are proposed. Using the logarithmic Sobolev inequality and Lyapunov mehtod, we obtain the general decay rates which are related to an ODE. Finally we give two examples to illustrate our results.

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Funding

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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Authors and Affiliations

  1. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, China

    Dandan Guo

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

    Zhifei Zhang

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

    Zhifei Zhang

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  1. Dandan Guo
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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 Dandan Guo and Zhifei Zhang. 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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Guo, D., Zhang, Z. General Decay for Semi-Linear Wave Equations with Memory Term and Logarithmic Source. Results Math 78, 117 (2023). https://doi.org/10.1007/s00025-023-01893-8

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