Boundary local null-controllability of the Kuramoto-Sivashinsky equation

Takéo Takahashi (1, 2)

1 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
2 IECL - Institut Élie Cartan de Lorraine

We prove that the Kuramoto-Sivashinsky equation is locally controllable in 1D and in 2D with one boundary control. Our method consists in combining several general results in order to reduce the null-controllability of this nonlinear parabolic equation to the exact controllability of a linear beam or plate system. This improves known results on the controllability of Kuramoto-Sivashinsky equation and gives a general strategy to handle the null-controllability of nonlinear parabolic systems.

Mots clés: null controllability 2010 Mathematics Subject Classification: 93B05; 35K55; Kuramoto-Sivashinsky equation; 93C10

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

Takéo Takahashi. Boundary local null-controllability of the Kuramoto-Sivashinsky equation. Mathematics of Control, Signals, and Systems, 2017, 29 (2), ⟨10.1007/s00498-016-0182-5⟩. ⟨hal-01373201⟩