Uniform stabilization of solutions of a nonlinear system of viscoelastic equations

Abstract

In this article, we are concerned with a system of two coupled viscoelastic equations which describes the interaction between two different fields arising in viscoelasticity. Under weaker conditions on the relaxation functions and for more general forms of nonlinearities, we extend and generalize some existing results, concerning the uniform decay for a single equation, to the case of a system.

Keywords:

• exponential decay
• memory type
• nonlocal
• polynomial decay
• relaxation function
• viscoelastic material

AMS 2000 Subject Classifications: :

• 35B37
• 35L55
• 74D05
• 93D15
• 93D20

Acknowledgement

The authors would like to express their sincere thanks to King Fahd University of Petroleum and Minerals for its support. This work has been funded by KFUPM under Project # SABIC-2006/01.