# American Institute of Mathematical Sciences

January  2019, 18(1): 159-180. doi: 10.3934/cpaa.2019009

## 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  September 2017 Revised  January 2018 Published  August 2018

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].

Citation: Mohammad M. Al-Gharabli, Aissa Guesmia, Salim A. Messaoudi. Existence and a general decay results for a viscoelastic plate equation with a logarithmic nonlinearity. Communications on Pure & Applied Analysis, 2019, 18 (1) : 159-180. doi: 10.3934/cpaa.2019009
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