简化的库拉莫托-西瓦申斯基稳定系统的边界可控性

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED Acta Applicandae Mathematicae Pub Date : 2023-12-12 DOI:10.1007/s10440-023-00626-x

Víctor Hernández-Santamaría, Alberto Mercado, Piero Visconti

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引用次数: 0

摘要

本文研究了二阶和四阶耦合抛物方程非线性系统的可控性。该系统可视为著名的稳定库拉莫托-西瓦申斯基系统的简化。我们只用了一个施加在二阶方程边界上的控制，就证明了如果二阶方程扩散系数的平方根是一个具有有限 Liouville-Roth 常数的无理数，则系统的局部空可控性成立。

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Boundary Controllability of a Simplified Stabilized Kuramoto-Sivashinsky System

In this paper, we study the controllability of a nonlinear system of coupled second- and fourth-order parabolic equations. This system can be regarded as a simplification of the well-known stabilized Kuramoto-Sivashinsky system. Using only one control applied on the boundary of the second-order equation, we prove that the local-null controllability of the system holds if the square root of the diffusion coefficient of the second-order equation is an irrational number with finite Liouville-Roth constant.

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来源期刊

Acta Applicandae Mathematicae 数学-应用数学

CiteScore

2.80

自引率

6.20%

发文量

审稿时长

16.2 months

期刊介绍： Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods. Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.