Local controllability of the stabilized Kuramoto-Sivashinsky system by a single control acting on the heat equation

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• 作者：Nicolá ; s Carreñ ; o ; ^{nicolas.carrenog@usm.cl" class="auth_mail" title="E-mail the corresponding author} ; Eduardo Cerpa ^{eduardo.cerpa@usm.cl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35K55 ; 93B05 ; 93C10
• 刊名：Journal de mathematiques pures et appliquees
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：106
• 期：4
• 页码：670-694
• 全文大小：487 K

文摘

In this paper we consider the so called stabilized Kuramoto–Sivashinsky system which couples a fourth order and a second order parabolic equations. We prove that this system is locally controllable to the trajectories by a single distributed control acting only on the heat equation. The main novelty is a new Carleman inequality for the solutions of a linear Kuramoto–Sivashinsky equation with nonhomogeneous boundary conditions.