General decay estimates for a Cauchy viscoelastic wave problem

Belkacem Said-Houari; Salim A. Messaoudi

doi:10.3934/cpaa.2014.13.1541

Article Contents

2014, Volume 13, Issue 4: 1541-1551. Doi: 10.3934/cpaa.2014.13.1541

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General decay estimates for a Cauchy viscoelastic wave problem

Belkacem Said-Houari^1, and
Salim A. Messaoudi^2,

1.
Division of Mathematical and Computer Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900
2.
King Fahd University of Petroleum and Minerals, Department of Mathematics and Statistics, Dhahran 31261

Received: August 2013

Revised: December 2013

Published: July 2015

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Abstract

In this paper, we consider the Cauchy problem of a viscoelatic wave equation and by using the energy method in the Fourier space, we show general decay estimates of the solution. This result improves and generalizes some other results in the literature.

Keywords:

Mathematics Subject Classification: Primary: 35L05, 35L15, 35L70; Secondary: 37B25.

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