General decay of the solution to a nonlinear viscoelastic modified von-Kármán system with delay

Ammar Khemmoudj; Yacine Mokhtari

doi:10.3934/dcds.2019155

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2019, Volume 39, Issue 7: 3839-3866. Doi: 10.3934/dcds.2019155

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General decay of the solution to a nonlinear viscoelastic modified von-Kármán system with delay

Ammar Khemmoudj^, and
Yacine Mokhtari

Faculty of Mathematics, University of Science and Technology Houari Boumedienne, P.O. Box 32, El-Alia 16111, Bab Ezzouar, Algiers, Algeria

^* Corresponding author: Ammar Khemmoudj
^* Corresponding author: Ammar Khemmoudj

Received: March 31, 2018

Revised: December 31, 2018

Published: April 2019

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Abstract

In this paper we consider a viscoelastic modified nonlinear Von-Kármán system with a linear delay term. The well posedness of solutions is proved using the Faedo-Galerkin method. We use minimal and general conditions on the relaxation function and establish a general decay results, from which the usual exponential and polynomial decay rates are only special cases.

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Mathematics Subject Classification: Primary: 35B40, 35L70, 49K25, 93D15, 93D20, 74K10.

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