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On a Semilinear Wave Equation with Kirchhoff-Type Nonlocal Damping Terms and Logarithmic Nonlinearity

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Abstract

The well-posedness and qualitative properties of the Dirichlet initial boundary value problem for a semilinear wave equation with Kirchhoff-type nonlocal damping terms and logarithmic nonlinearity are considered in this paper. By improving Faedo–Galerkin approximation technique, together with potential well theory and energy perturbation technique, we establish well-posedness of local and global solutions, as well as the algebraic and exponential decay estimates of the energy. Meanwhile, based on contradiction argument and auxiliary function method, we show the finite time blow-up of the solution with negative initial energy.

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Acknowledgements

The authors would like to deeply thank all the reviewers for their insightful and constructive comments.

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  1. School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, China

    Yi Yang & Zhong Bo Fang

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  1. Yi Yang
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  2. Zhong Bo Fang
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Correspondence to Zhong Bo Fang.

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This work is supported by the Natural Science Foundation of Shandong Province of China (Grant No. ZR2019MA072).

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Yang, Y., Fang, Z.B. On a Semilinear Wave Equation with Kirchhoff-Type Nonlocal Damping Terms and Logarithmic Nonlinearity. Mediterr. J. Math. 20, 13 (2023). https://doi.org/10.1007/s00009-022-02221-0

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  • DOI: https://doi.org/10.1007/s00009-022-02221-0

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