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

2022/12/27 by Roberto de A. Capistrano–Filho, Capistrano-Filho, Roberto de A., Victor H. Gonzalez Martinez +3
Computer Science · Engineering · Mathematics · #35Q53 #93C20 #93D15 #93D30 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2212.13552

openalex publication_date 2022/12/27 · openalex created_date 2023/01/06 · openalex updated_date 2026/07/28

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.

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