Decay of energy for wave equations with strong damping terms and space–time-dependent coefficients

Abstract

We study the asymptotic behaviour of solutions to the wave equations with strong damping terms and space–time-dependent coefficients by establishing decay estimates for the total energy of solutions.

Keywords:

• wave equation with strong damping term
• space–time-dependent coefficients
• decay rate of energy

AMS Subject Classifications:

• Primary 35L05
• 35L70
• Secondary 37L15

Acknowledgments

The authors are grateful to Prof. Grozdena Todorova and Prof. Borislav Yordanov from the University of Tennessee, Knoxville, for their many valuable helps and supports. The third author wish to thank the department of mathematics, University of Tennessee-Knoxville for its kind hospitality. The authors also would like to thank the referees for their careful reading and useful comments.