Stability of the Kawahara equation with time-varying delay

Articles in Press

Document Type : Research Article

Authors

1 Universit\'e Oran1 Ahmed Ben Bella, Laboratoire de Mathématique et ses Applications, Oran, Algeria

2 Université Oran1 Ahmed Ben Bella, Laboratoire de Mathématique et ses Applications, Oran, Algeria

Abstract

In this work, we consider the nonlinear Kawahara equation with internal time-dependent delay in a bounded domain. We prove that this equation has a unique solution. Moreover, we use a Lyapunov functional approach to prove the exponential stability of the nonlinear system, under some assumptions on the weights of the feedbacks and on the time-dependent delay. We present some numerical simulations to illustrate the obtained results.

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Journal of Mathematical Modeling

Articles in Press, Corrected Proof
Available Online from 04 February 2025

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