Insensitizing control problem for the Hirota–Satsuma system of KdV–KdV type

0578002 - MÚ 2025 RIV GB eng J - Journal Article
Bhandari, Kuntal
Insensitizing control problem for the Hirota–Satsuma system of KdV–KdV type.
Nonlinear Analysis: Theory, Methods & Applications. Roč. 239, February (2024), č. článku 113422. ISSN 0362-546X. E-ISSN 1873-5215
R&D Projects: GA ČR(CZ) GC22-08633J
Institutional support: RVO:67985840
Keywords : Korteweg-de Vries system * insensitizing control * Carleman estimate * inverse mapping theorem
OECD category: Pure mathematics
Impact factor: 1.4, year: 2022
Method of publishing: Limited access
https://doi.org/10.1016/j.na.2023.113422

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.
Permanent Link: https://hdl.handle.net/11104/0347057