Remark on the global null controllability for a viscous Burgers-particle system with particle supported control

Mythily Ramaswamy (1) , Arnab Roy (2) , Takéo Takahashi (3, 4)

1 Chennai Mathematical Institute [Inde]
2 IM / CAS - Institute of Mathematics of the Czech Academy of Science
3 IECL - Institut Élie Cartan de Lorraine
4 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization

This paper is devoted to study the controllability of a one-dimensional fluid-particle interaction model where the fluid follows the viscous Burgers equation and the point mass obeys Newton's second law. We prove the null controllability for the velocity of the fluid and the particle and an approximate controllability for the position of the particle with a control variable acting only on the particle. One of the novelties of our work is the fact that we achieve this controllability result in a uniform time for all initial data and without any smallness assumptions on the initial data.

Mots clés: viscous Burgers equation; Fluid-structure interaction; global controllability

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Mythily Ramaswamy, Arnab Roy, Takéo Takahashi. Remark on the global null controllability for a viscous Burgers-particle system with particle supported control. Applied Mathematics Letters, 2020, ⟨10.1016/j.aml.2020.106483⟩. ⟨hal-02541031⟩