A general decay result of a coupled system of nonlinear wave equations

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Abstract

This work is concerned with a nonlinear system of two coupled viscoelastic equations. Under some restrictions on the coupled functions, we establish, for a wider class of relaxation functions, a generalized stability result for this system. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl Anal 87(3): 247–263, 2008) and Liu (Non-linear Anal 71, 2257–2267, 2009).

Keywords

General decay Relaxation function Nonlinear Wave equation Viscoelasticity 

Mathematics Subject Classification

35L05 35L20 35L70 35L53 35B40 

Notes

Acknowledgements

The authors thank KFUPM for its continuous support. This work was funded by KFUPM under Project # IN151025.

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Copyright information

© Springer-Verlag Italia 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia

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