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- Title
Controllability of a simplified time-discrete stabilized Kuramoto-Sivashinsky system.
- Authors
Hernández-Santamaría, Víctor
- Abstract
In this paper, we study some controllability and observability properties for a coupled system of time-discrete fourth- and second-order parabolic equations. This system can be regarded as a simplification of the well-known stabilized Kumamoto-Sivashinsky equation. Unlike the continuous case, we can prove only a relaxed observability inequality which yields a $ \phi(\triangle t) $-controllability result. This result tells that we cannot reach exactly zero but rather a small target whose size goes to 0 as the discretization parameter $ \triangle t $ goes to 0. The proof relies on a known Carleman estimate for second-order time-discrete parabolic operators and a new Carleman estimate for the time-discrete fourth-order equation.
- Subjects
CONTROLLABILITY in systems engineering; OBSERVABILITY (Control theory); CARLEMAN theorem; PARABOLIC operators
- Publication
Evolution Equations & Control Theory, 2023, Vol 12, Issue 2, p1
- ISSN
2163-2472
- Publication type
Article
- DOI
10.3934/eect.2022038