On the controllability of parabolic equations with large parameters in small time

IF 2.5 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters Pub Date : 2025-07-14 DOI:10.1016/j.sysconle.2025.106177

F.W. Chaves-Silva , N. Carreño , M.G. Ferreira-Silva

引用次数: 0

Abstract

In this work, we deal with the heat equation perturbed by an anomalous diffusion term scaled by a large parameter. More precisely, we study the cost of null controllability for the system as the parameter goes to infinity. We show that is possible to construct null controls that exhibit exponential decay with respect to the parameter. Our study gives a positive answer to a conjecture raised by J.-L. Lions and E. Zuazua [Rev. Mat. Univ. Complut. Madrid, 10 (2)(1997), 481-524]. Additionally, using the so-called source term method and an inverse mapping theorem, we prove that it is possible to achieve controllability results for certain nonlinear systems with a control with a cost decaying to zero as well.

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大参数抛物型方程在小时间内的可控性

在这项工作中，我们处理了由一个大参数缩放的异常扩散项扰动的热方程。更确切地说，我们研究了当参数趋于无穷时系统的无可控性代价。我们表明，可以构造相对于参数表现出指数衰减的零控制。我们的研究对j.l提出的一个猜想给出了肯定的答案。狮子和E. Zuazua [Rev. Mat. university . Complut.]马德里，10(2)(1997),481-524。此外，利用源项法和逆映射定理，证明了对于代价衰减为零的非线性控制系统，也有可能获得可控结果。

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

Systems & Control Letters 工程技术-运筹学与管理科学

CiteScore

4.60

自引率

3.80%

发文量

144

审稿时长

6 months

期刊介绍： Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.