耦合退化波方程的间接边界可控性

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED Acta Applicandae Mathematicae Pub Date : 2024-04-12 DOI:10.1007/s10440-024-00649-y

Alhabib Moumni, Jawad Salhi, Mouhcine Tilioua

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引用次数: 0

摘要

在本文中，我们考虑了一个由两个退化波方程组成的、通过速度耦合的系统，其中只有一个是可控的。我们假设耦合参数足够小，并将重点放在空可控性问题上。为此，我们首先利用乘法器技术和谨慎的能量估计，建立了相应邻接系统的间接可观测性估计。然后，通过应用希尔伯特唯一性方法，我们证明原系统的间接边界可控性在足够大的时间内成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Indirect Boundary Controllability of Coupled Degenerate Wave Equations

In this paper, we consider a system of two degenerate wave equations coupled through the velocities, only one of them being controlled. We assume that the coupling parameter is sufficiently small and we focus on null controllability problem. To this aim, using multiplier techniques and careful energy estimates, we first establish an indirect observability estimate for the corresponding adjoint system. Then, by applying the Hilbert Uniqueness Method, we show that the indirect boundary controllability of the original system holds for a sufficiently large time.

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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.