Exponential energy decay of solutions for a system of viscoelastic wave equations of Kirchhoff type with strong damping

Abstract

The initial boundary value problem for a system of viscoelastic wave equations of Kirchhoff type with strong damping is considered. We prove that, under suitable assumptions on relaxation functions and certain initial data, the decay rate of the solutions energy is exponential.

Keywords:

• viscoelastic wave equation
• Kirchhoff type
• strong damping
• exponential decay

AMS Subject Classifications::

• 35B40
• 35L70
• 35L53

Acknowledgements

This work was partly supported by the Tianyuan Fund of Mathematics (Grant No. 11026211) and the Natural Science Foundation of the Jiangsu Higher Education Institutions (Grant No. 09KJB110005).