"Null Controllability of the stabilized kuramoto-sivashinsky system with one distributed control"

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Year:
2015
Type of Publication:
Article
Authors:
Journal:
SIAM Journal Control Optim
Volume:
53
Number:
3
Pages:
1543-1568
Abstract:
This paper presents a control problem for a one-dimensional nonlinear parabolic system, which consists of a Kuramoto--Sivashinsky--Korteweg de Vries equation coupled to a heat equation. We address the problem of controllability by means of a control supported in an interior open subset of the domain and acting on one equation only. The local null-controllability of the system is proved. The proof is based on a Carleman estimate for the linearized system around the origin. A local inversion theorem is applied to get the result for the nonlinear system.