Uniform decay for wave equations with weakly dissipative boundary feedback

Abstract

In this paper, we consider a wave equation with a nonlinear weakly dissipative boundary feedback localized on a part of the boundary. We establish an explicit and general decay rate result, using some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term.

Keywords:

• general decay
• boundary damping
• weak dissipation, wave equation
• convexity

AMS Classification:

• 35B37
• 35L55
• 74D05
• 93D15
• 93d20

Acknowledgements

The author thanks KFUPM for its continuous support.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work has been funded by KFUPM under Project #IN121046.