Local null-controllability of a system coupling Kuramoto-Sivashinsky-KdV and elliptic equations

0570784 - MÚ 2024 RIV US eng J - Journal Article
Bhandari, Kuntal - Majumdar, S.
Local null-controllability of a system coupling Kuramoto-Sivashinsky-KdV and elliptic equations.
Journal of Mathematical Analysis and Applications. Roč. 525, č. 1 (2023), č. článku 127213. ISSN 0022-247X. E-ISSN 1096-0813
Institutional support: RVO:67985840
Keywords : Carleman estimates * fixed point argument * KS-KdV-elliptic system * null-controllability
OECD category: Pure mathematics
Impact factor: 1.3, year: 2022
Method of publishing: Limited access
https://doi.org/10.1016/j.jmaa.2023.127213

This paper deals with the null-controllability of a system of mixed parabolic-elliptic pdes at any given time T>0. More precisely, we consider the Kuramoto-Sivashinsky–Korteweg-de Vries equation coupled with a second order elliptic equation posed in the interval (0,1). We first show that the linearized system is globally null-controllable by means of a localized interior control acting on either the KS-KdV or the elliptic equation. Using the Carleman approach, we provide the existence of a control with the explicit cost CeC/T with some constant C>0 independent in T. Then, applying the source term method developed in [39], followed by the Banach fixed point theorem, we conclude the small-time local null-controllability result of the nonlinear system.
Permanent Link: https://hdl.handle.net/11104/0342124