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Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term

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Abstract

In this paper, we consider a plate equation with a logarithmic nonlinearity in the presence of nonlinear frictional damping. Using the Galaerkin method, we establish the existence of solutions of the problem and we prove an explicit and general decay rate result, using the multiplier method and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term.

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Change history

  • 08 August 2019

    Due to an error in the typesetting process, reference [1] is incorrectly published in the original publication of the article.

  • 08 August 2019

    Due to an error in the typesetting process, reference [1] is incorrectly published in the original publication of the article.

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Authors and Affiliations

  1. The Preparatory Year Program, Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Mohammad M. Al-Gharabli

  2. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Salim A. Messaoudi

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

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Al-Gharabli, M.M., Messaoudi, S.A. Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term. J. Evol. Equ. 18, 105–125 (2018). https://doi.org/10.1007/s00028-017-0392-4

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  • DOI: https://doi.org/10.1007/s00028-017-0392-4

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