Volume 29, 2023
|Number of page(s)||20|
|Published online||26 April 2023|
Small-time global null controllability of generalized Burgers’ equations
Laboratoire Jacques-Louis Lions, Sorbonne Université, Paris, France
* Corresponding author: firstname.lastname@example.org
Accepted: 26 March 2023
In this paper, we study the small-time global null controllability of the generalized Burgers’ equations yt + γ|y|γ-1 yx — yxx = 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 globally null controllable. Our proof relies on the return method and a careful analysis of the shape and dissipation of a boundary layer.
Mathematics Subject Classification: 93B05
Key words: Controllability / Burgers equation / boundary layer
© The authors. Published by EDP Sciences, SMAI 2023
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