Existence and a general decay results for a viscoelastic plate equation with a logarithmic nonlinearity

Mohammad M. Al-Gharabli; Aissa Guesmia; Salim A. Messaoudi

doi:10.3934/cpaa.2019009

Article Contents

2019, Volume 18, Issue 1: 159-180. Doi: 10.3934/cpaa.2019009

This issue Previous Article Bounded state solutions of Kirchhoff type problems with a critical exponent in high dimension Next Article Kirchhoff type equations with strong singularities

Existence and a general decay results for a viscoelastic plate equation with a logarithmic nonlinearity

1.
King Fahd University of Petroleum and Minerals, The Preparatory Year Program, Department of Mathematics, Dhahran 31261, Saudi Arabia
2.
Institut Elie Cartan de Lorraine, UMR 7502, Université de Lorraine, 3 Rue Augustin Fresnel, BP 45112, 57073 Metz Cedex 03, France
3.
King Fahd University of Petroleum and Minerals, Department of Mathematics and Statistics, Dhahran 31261, Saudi Arabia

Received: August 31, 2017

Revised: December 31, 2017

Published: August 2018

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Abstract

In this paper, we consider a viscoelastic plate equation with a logarithmic nonlinearity. Using the Galaerkin method and the multiplier method, we establish the existence of solutions and prove an explicit and general decay rate result. This result extends and improves many results in the literature such as Gorka [19], Hiramatsu et al. [27] and Han and Wang [26].

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Mathematics Subject Classification: 35B35, 35L55, 75D05, 74D10, 93D20.

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References

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