Work

Approximate controllability and irreducibility of the 2D Zakharov–Kuznetsov–Burgers equation

Year: 2025

Type: article

Abstract: The present paper is a continuation of [Chen and Rosier, Discrete Continuous Dyn. Syst.- B 25 (2020) 3889–3916] and [Chen, Appl. Math. Optim. 87 (2023) 12]. In this paper, we consider the 2D Zakharov–Kuznetsov–Burgers equation posed on the periodic domain T2. We show that the 2D Zakharov–Kuznetsov–Burgers equation is globally approximately controllable by a finite dimensional external force, the proof is based on the Agrachev–Sarychev approach in geometric control theory. As an application of the approximate controllability result, we establish the irreducibility of the transition semigroup associated with stochastic Zakharov–Kuznetsov–Burgers equation driven by a degenerate noise.

Source: ESAIM Control Optimisation and Calculus of Variations

DOI: 10.1051/cocv/2025063

Author: Mo Chen

Institution: Northeast Normal University

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid:

Funders: People's Government of Jilin Province, Fundamental Research Funds for the Central Universities