General decay for a class of viscoelastic problem with not necessarily decreasing kernel

ABSTRACT

In this paper, a problem which arises in a class of viscoelasticity is considered. We obtain the decay rate of the energy, for certain class of relaxation functions not necessarily exponentially or polynomially decaying to zero.

KEYWORDS:

• General decay
• viscoelastic equation
• exponential decay
• polynomial decay

AMS SUBJECT CLASSIFICATIONS:

• 35L05
• 35L15
• 35L70

Acknowledgements

The authors would like to thank the anonymous referees and the handling editor for their careful reading and for relevant remarks/suggestions which helped them to improve the paper. The second author gratefully acknowledge Qassim University in Kingdom of Saudi Arabia and this presented work is in memory of his father (1910–1999) Mr. Mahmoud ben Mouha Boulaaras.

Notes

No potential conflict of interest was reported by the authors.