Small-time global null controllability of generalized Burgers' equations

2022/06/13 by Rémi Robin, Robin, Rémi · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.2206.05931

openalex publication_date 2022/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the small-time global null controllability of the generalized Burgers' equations y_t + γ|y|^γ-1y_x-y_xx=u(t) on the segment [0,1]. The scalar control u(t) is uniform in space and plays a role similar to the pressure in higher dimension. We set a right Dirichlet boundary condition y(t,1)=0, and allow a left boundary control y(t,0)=v(t). Under the assumption γ>3/2 we prove that the system is small-time global null controllable. Our proof relies on the return method and a careful analysis of the shape and dissipation of a boundary layer.

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