Open AccessOn the asymptotic stability of the Korteweg-de Vries equation with time-delayed internal feedback
Author(s) -
Julie Valein
Publication year - 2022
Publication title -
mathematical control and related fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.658
H-Index - 21
eISSN - 2156-8472
pISSN - 2156-8499
DOI - 10.3934/mcrf.2021039
Subject(s) - term (time) , exponential stability , mathematics , stability (learning theory) , nonlinear system , korteweg–de vries equation , exponential function , control theory (sociology) , mathematical analysis , physics , computer science , control (management) , quantum mechanics , machine learning , artificial intelligence
The aim of this work is to study the asymptotic stability of the nonlinear Korteweg-de Vries equation in the presence of a delayed term in the internal feedback. We first consider the case where the weight of the term with delay is smaller than the weight of the term without delay and we prove a semiglobal stability result for any lengths. Secondly we study the case where the support of the term without delay is not included in the support of the term with delay. In that case, we give a local exponential stability result if the weight of the delayed term is small enough. We illustrate these results by some numerical simulations.