Energy decay for a weakly nonlinear damped porous system with a nonlinear delay

Abstract

This paper considers a one-dimensional porous system damped with weakly nonlinear feedback in the presence of a nonlinear delay. We prove the global existence and uniqueness results using the Faedo–Galerkin procedure. Furthermore, under appropriate assumptions on the weight of the delay and without imposing any restrictive growth assumption on the damping term at the origin, we establish an energy decay rate, using a perturbed energy method and some properties of convex functions in case of the same speed of propagation in the two equations of the system.

Keywords:

• Porous system
• energy decay
• nonlinear damping
• delay

2010 Mathematics Subject Classification::

• 35B35
• 35B40
• 93D20

Acknowledgments

The first author extends his appreciation to the University of Hafr Al-Batin (UHB) for the continuous support. The University of Sharjah supports the second author under Project # 1802144069. The authors are grateful to the anonymous referee for careful readings and helpful comments.

Disclosure statement

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

Data availability statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Additional information

Funding

The first author extends his appreciation to UHB for the continuous support. The University of Sharjah supports the second author under Project # 1802144069. The authors are grateful to the anonymous referee for careful readings and helpful comments.