Insensitizing control problem for the Hirota-Satsuma system of KdV-KdV type
Abstract
This paper is concerned with the existence of insensitizing controls for a nonlinear coupled system of two Korteweg-de Vries (KdV) equations, typically known as the Hirota-Satsuma system. The idea is to look for controls such that some functional of the states (the so-called sentinel) is insensitive to the small perturbations of initial data. Since the system is coupled, we consider a sentinel in which we observe both components of the system in a localized observation set. By some classical argument, the insensitizing problem is then reduced to a null-control problem for an extended system where the number of equations is doubled. We study the null-controllability for the linearized model associated to that extended system by means of a suitable Carleman estimate which is proved in this paper. Finally, the local null-controllability of the extended (nonlinear) system is obtained by applying the inverse mapping theorem, and this implies the required insensitizing property for the concerned model.
Keywords
Cite
@article{arxiv.2306.08497,
title = {Insensitizing control problem for the Hirota-Satsuma system of KdV-KdV type},
author = {Kuntal Bhandari},
journal= {arXiv preprint arXiv:2306.08497},
year = {2023}
}