2021/03/23 by Víctor Hernández-Santamaría, Hernández-Santamaría, Víctor · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations #math.AP
paper · pdf · doi:10.48550/arxiv.2103.12238
arxiv created 2021/03/23 · openalex publication_date 2021/03/23 · arxiv updated 2021/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ϕ(\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.