Exact controllability for a degenerate and singular wave equation with moving boundary

IF 1.1 Q2 MATHEMATICS, APPLIED

Numerical Algebra Control and Optimization Pub Date : 2022-01-01 DOI:10.3934/naco.2022001

Alhabib Moumni, J. Salhi

引用次数: 1

Abstract

This paper is concerned with the exact boundary controllability for a degenerate and singular wave equation in a bounded interval with a moving endpoint. By the multiplier method and using an adapted Hardy-poincaré inequality, we prove direct and inverse inequalities for the solutions of the associated adjoint equation. As a consequence, by the Hilbert Uniqueness Method, we deduce the controllability result of the considered system when the control acts on the moving boundary. Furthermore, improved estimates of the speed of the moving endpoint and the controllability time are obtained.

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一类带运动边界的简并奇异波动方程的精确可控性

研究了带运动端点的有界区间内简并奇异波动方程的精确边界可控性。利用乘数法，利用hardy - poincarcarve不等式，证明了伴随方程解的正不等式和逆不等式。因此，利用Hilbert唯一性方法，我们推导出了当控制作用于运动边界时所考虑系统的可控性结果。在此基础上，改进了对运动端点速度和可控性时间的估计。

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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来源期刊

Numerical Algebra Control and Optimization MATHEMATICS, APPLIED-

CiteScore

3.10

自引率

0.00%

发文量

期刊介绍： Numerical Algebra, Control and Optimization (NACO) aims at publishing original papers on any non-trivial interplay between control and optimization, and numerical techniques for their underlying linear and nonlinear algebraic systems. Topics of interest to NACO include the following: original research in theory, algorithms and applications of optimization; numerical methods for linear and nonlinear algebraic systems arising in modelling, control and optimisation; and original theoretical and applied research and development in the control of systems including all facets of control theory and its applications. In the application areas, special interests are on artificial intelligence and data sciences. The journal also welcomes expository submissions on subjects of current relevance to readers of the journal. The publication of papers in NACO is free of charge.