Stabilization of the Kawahara-Kadomtsev-Petviashvili equation with time-delayed feedback

TL;DR

This paper proves that the Kawahara-Kadomtsev-Petviashvili equation can be exponentially stabilized using damping and delay feedback, identifying optimal constants and minimal times for energy decay.

Contribution

It introduces two approaches to establish exponential stability and determines optimal constants and minimal times for stabilization of the equation.

Findings

Solutions are locally and globally exponentially stable under damping and delay.

The optimal constant and minimal time for energy decay are explicitly derived.

Stability results are achieved using two different analytical approaches.

Abstract

Results of stabilization for the higher order of the Kadomtsev-Petviashvili equation are presented in this manuscript. Precisely, we prove with two different approaches that under the presence of a damping mechanism and an internal delay term (anti-damping) the solutions of the Kawahara-Kadomtsev-Petviashvili equation are locally and globally exponentially stable. The main novelty is that we present the optimal constant, as well as the minimal time, that ensures that the energy associated with this system goes to zero exponentially.