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

Part of: Control systems Equations of mathematical physics and other areas of application Stability

Published online by Cambridge University Press:  11 September 2023

Roberto de A. Capistrano–Filho Open the ORCID record for Roberto de A. Capistrano–Filho [Opens in a new window] ,
Victor Hugo Gonzalez Martinez  and
Juan Ricardo Muñoz
Roberto de A. Capistrano–Filho
Affiliation:
Departamento de Matemática, Universidade Federal de Pernambuco (UFPE), 50740-545, Recife PE, Brazil (roberto.capistranofilho@ufpe.br; victor.martinez@ufpe.br; juan.ricardo@ufpe.br)
Victor Hugo Gonzalez Martinez
Affiliation:
Departamento de Matemática, Universidade Federal de Pernambuco (UFPE), 50740-545, Recife PE, Brazil (roberto.capistranofilho@ufpe.br; victor.martinez@ufpe.br; juan.ricardo@ufpe.br)
Juan Ricardo Muñoz
Affiliation:
Departamento de Matemática, Universidade Federal de Pernambuco (UFPE), 50740-545, Recife PE, Brazil (roberto.capistranofilho@ufpe.br; victor.martinez@ufpe.br; juan.ricardo@ufpe.br)
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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 of this work 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.

Keywords

KP systemdelayed systemdamping mechanismstabilization

MSC classification

Primary: 35Q53: KdV-like equations (Korteweg-de Vries)
Secondary: 93D15: Stabilization of systems by feedback 93D30: Scalar and vector Lyapunov functions 93C20: Systems governed by partial differential equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 27
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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