Energy decay in a viscoelastic equation with past history and boundary feedback

ABSTRACT

In this paper, we consider a viscoelastic equation with nonlinear feedback localized on a part of the boundary and in the presence of infinite-memory term. With imposing a more general condition on the relaxation function, we establish a more general stability result that generalizes and improves many earlier results in the literature. Our results are obtained without imposing any restrictive growth assumption on the damping term and without using any assumption on the boundedness of initial data used in many earlier papers in the literature.

COMMUNICATED BY:

• Y. Ou

KEYWORDS:

• Stability
• convex functions
• infinite memory
• viscoelasticity

AMS CLASSIFICATIONS:

• 35B37
• 35L55
• 74D05
• 93D15
• 93D20

Acknowledgments

The authors thank KFUPM and the referee for her/his very careful reading and valuable comments. This work is funded by KFUPM under Project #SB191037.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is funded by King Fahd University of Petroleum and Minerals (KFUPM) under Project no. SB191037.