具有漂移和奇异势的一维退化抛物方程的边界可控性

IF 1 4区数学 Q1 MATHEMATICS

Mathematical Control and Related Fields Pub Date : 2023-02-02 DOI:10.3934/mcrf.2023027

Leandro Galo-Mendoza, Marcos L'opez-Garc'ia

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引用次数: 1

摘要

证明了一类具有漂移和奇异势的一维退化抛物方程的零可控性。在这里，我们考虑一个加权的诺伊曼边界控制在左端点，在那里产生的潜力。我们使用在加权Sobolev空间中定义的合适算子的谱分解和Fattorini和Russell的矩方法来获得可控性代价的上限估计。利用指数型解析函数的表示定理，我们也得到了可控性代价的一个较低估计。

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Boundary controllability for a 1D degenerate parabolic equation with drift and a singular potential

We prove the null controllability of a one-dimensional degenerate parabolic equation with drift and a singular potential. Here, we consider a weighted Neumann boundary control at the left endpoint, where the potential arises. We use a spectral decomposition of a suitable operator, defined in a weighted Sobolev space, and the moment method by Fattorini and Russell to obtain an upper estimate of the cost of controllability. We also obtain a lower estimate of the cost of controllability by using a representation theorem for analytic functions of exponential type.

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来源期刊

Mathematical Control and Related Fields MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

8.30%

发文量

期刊介绍： MCRF aims to publish original research as well as expository papers on mathematical control theory and related fields. The goal is to provide a complete and reliable source of mathematical methods and results in this field. The journal will also accept papers from some related fields such as differential equations, functional analysis, probability theory and stochastic analysis, inverse problems, optimization, numerical computation, mathematical finance, information theory, game theory, system theory, etc., provided that they have some intrinsic connections with control theory.