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

2022/08/25 by Kuntal Bhandari, Bhandari, Kuntal, Subrata Majumdar +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2208.12213

openalex publication_date 2022/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

This paper deals with the null-controllability of a system of \em 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 Ce^C/T with some constant C>0 independent in T. Then, applying the source term method followed by the Banach fixed point theorem, we conclude the small-time local null-controllability result of the nonlinear systems.

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