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

2020/04/12 by Mythily Ramaswamy, Arnab Roy, Ramaswamy, Mythily +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2004.05626

openalex publication_date 2020/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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