General decay of solutions to a viscoelastic wave equation with linear damping, nonlinear damping and source term

ABSTRACT

This paper is concerned with the decay property of a nonlinear viscoelastic wave equation with linear damping, nonlinear damping and source term. Under weaker assumption on the relaxation function, we establish a general decay result, which extends the result obtained in Messaoudi [Exponential decay of solutions of a nonlinearly damped wave equation. Nodea-Nonlinear Differ Equat Appl. 2005;12:391–399].

Keywords:

• General decay
• viscoelastic wave equation
• source term

2010 Mathematics Subject Classifications:

• 35L05
• 35L15
• 35L70
• 35B25

Acknowledgments

The authors would like to extend their sincere appreciation to the Hubei Key Laboratory of Computational Science at Wuhan university.

Disclosure statement

No potential conflict of interest was reported by the authors.