Geodesic
On the control of the linear Kuramoto−Sivashinsky equation
Cerpa, Eduardo1  ; Guzmán, Patricio1 ; Mercado, Alberto1 
1 Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 1, pp. 165-194

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In this paper we study the null controllability property of the linear Kuramoto−Sivashinsky equation by means of either boundary or internal controls. In the Dirichlet boundary case, we use the moment theory to prove that the null controllability property holds with only one boundary control if and only if the anti-diffusion parameter of the equation does not belong to a critical set of parameters. Regarding the Neumann boundary case, we prove that the null controllability property does not hold with only one boundary control. However, it does always hold when either two boundary controls or an internal control are considered. The proof of the latter is based on the controllability-observability duality and a suitable Carleman estimate.

DOI : 10.1051/cocv/2015044
Classification : 35K35, 93B05
Keywords: Kuramoto−Sivashinky equation, parabolic equation, boundary control, internal control, null controllability, moment theory, Carleman estimates

Cerpa, Eduardo 1 ; Guzmán, Patricio 1 ; Mercado, Alberto 1

1 Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile. 
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Cerpa, Eduardo; Guzmán, Patricio; Mercado, Alberto. On the control of the linear Kuramoto−Sivashinsky equation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 1, pp. 165-194. doi: 10.1051/cocv/2015044

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