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Small time global null controllability for a viscous Burgers' equation despite the presence of a boundary layer

Abstract : In this work, we are interested in the small time global null controllability for the viscous Burgers' equation y_t - y_xx + y y_x = u(t) on the line segment [0,1]. The second-hand side is a scalar control playing a role similar to that of a pressure. We set y(t,1) = 0 and restrict ourselves to using only two controls (namely the interior one u(t) and the boundary one y(t,0)). In this setting, we show that small time global null controllability still holds by taking advantage of both hyperbolic and parabolic behaviors of our system. We use the Cole-Hopf transform and Fourier series to derive precise estimates for the creation and the dissipation of a boundary layer.
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https://hal.archives-ouvertes.fr/hal-00776508
Contributor : Frédéric Marbach <>
Submitted on : Wednesday, January 18, 2017 - 12:06:33 PM
Last modification on : Monday, March 15, 2021 - 9:50:22 AM
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Frédéric Marbach. Small time global null controllability for a viscous Burgers' equation despite the presence of a boundary layer. Journal de Mathématiques Pures et Appliquées, Elsevier, 2014, 102 (2), pp.364-384. ⟨10.1016/j.matpur.2013.11.013⟩. ⟨hal-00776508⟩

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