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Some Existence and Exponential Stability Results for a Plate Equation with Strong Damping and a Logarithmic Source Term

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Abstract

In this paper, we consider a plate equation with a strong damping and a logarithmic nonlinearity. Using the Galerkin method, we establish the existence of the solutions of the problem and we prove an exponential decay result, using the multiplier method. This result extends and improves many results in the literature.

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Acknowledgements

The authors thank KFUPM for its continuous support. This work was funded by KFUPM under Project #INCB2205.

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Authors and Affiliations

  1. The Preparatory Year Program and The Interdisciplinary Research Center in Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Mohammad M. Al-Gharabli

  2. Institut Elie Cartan de Lorraine, UMR 7502, Université de Lorraine, 3 Rue Augustin Fresnel, BP 45112, 57073, Metz Cedex 03, France

    Aissa Guesmia

  3. Department of Mathematics, University of Sharjah, P. O. Box, 27272, Sharjah, United Arab Emirates

    Salim A. Messaoudi

Authors
  1. Mohammad M. Al-Gharabli
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  2. Aissa Guesmia
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  3. Salim A. Messaoudi
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Correspondence to Mohammad M. Al-Gharabli.

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Al-Gharabli, M.M., Guesmia, A. & Messaoudi, S.A. Some Existence and Exponential Stability Results for a Plate Equation with Strong Damping and a Logarithmic Source Term. Differ Equ Dyn Syst (2022). https://doi.org/10.1007/s12591-022-00625-8

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  • DOI: https://doi.org/10.1007/s12591-022-00625-8

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