Polynomial stability of solutions for a system of non-linear viscoelastic equations

Abstract

In this article, we consider an interacting system consisting of two weakly-coupled viscoelastic equations. This work proves a uniform stabilization result without assuming any decay rate of the relaxation function provided that the kernels have some flat zones, the size of the flat zones are sufficiently small.

Keywords:

• viscoelasticity
• memory term
• flat zone
• polynomial decay

AMS Subject Classifications:

• 35B40
• 35L70

Acknowledgements

This work was supported by PRC Grants NSFC 10771032. The author expresses his gratitude to Professor Mingxin Wang for his enthusiastic guidance and constant encouragement.