Singular Perturbation Analysis for a Coupled KdV-ODE System

• 成果类型: Article
• 署名作者: Marx, Swann; Cerpa, Eduardo
• 署名单位: Nantes Universite; Ecole Centrale de Nantes; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); Pontificia Universidad Catolica de Chile
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3359538
• 发表日期: 2024
• 页码: 5326-5337
• 关键词: Automatic control; Distributed parameter systems; partial differential equations (PDEs)

摘要

Asymptotic stability is with no doubts an essential property to be studied for any system. This analysis often becomes very difficult for coupled systems and even harder when different time-scales appear. The singular perturbation method allows to decouple a full system into what are called the reduced-order system and the boundary layer system to get simpler stability conditions for the original system. In the infinite-dimensional setting, we do not have a general result making sure this strategy works. This article is devoted to this analysis for some systems coupling the Korteweg-de Vries equation and an ordinary differential equation with different time scales. More precisely, we obtain stability results and Tikhonov-type theorems.