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General Decay Rates for a Viscoelastic Wave Equation with Dynamic Boundary Conditions and Past History

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Abstract

In this paper, we study a viscoelastic wave equation with dynamic boundary conditions, source term and a nonlinear weak damping localized on a part of the boundary and past history. Under suitable assumptions, we establish an explicit and general decay result of energy by introducing suitable energy and perturbed Lyapunov functionals and some properties of convex functions.

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Acknowledgements

The author expresses his sincere thanks to the anonymous referee for his/her constructive remarks that helped to improve this paper. This work was supported by the National Natural Science Foundation of China (No. 11701465).

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  1. Department of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, People’s Republic of China

    Baowei Feng

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  1. Baowei Feng
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Feng, B. General Decay Rates for a Viscoelastic Wave Equation with Dynamic Boundary Conditions and Past History. Mediterr. J. Math. 15, 103 (2018). https://doi.org/10.1007/s00009-018-1154-4

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  • DOI: https://doi.org/10.1007/s00009-018-1154-4

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