On the Exact Global Controllability of a Semilinear Evolution Equation

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2024-07-08 DOI:10.1134/s0012266124030091

A. V. Chernov

引用次数: 0

Abstract

For the Cauchy problem associated with a controlled semilinear evolution equation with an operator (not necessarily bounded) in a Hilbert space, we obtain sufficient conditions for exact controllability into a given terminal state (and also into given intermediate states at interim time moments) on an arbitrarily fixed (without additional constraints) time interval. Here we use the Browder—Minty theorem and also a chain technology of successive continuation of the solution of the controlled system to intermediate states. As examples, we consider a semilinear pseudoparabolic equation and a semilinear wave equation.

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论半线性演化方程的精确全局可控性

摘要对于与希尔伯特空间中带有算子（不一定是有界的）的受控半线性演化方程相关的考奇问题，我们获得了在任意固定（无附加约束）时间间隔上精确可控性进入给定终态（以及在中间时刻进入给定中间状态）的充分条件。在这里，我们使用了布劳德-明蒂定理（Browder-Minty theorem），以及受控系统解连续延续到中间状态的链式技术。作为示例，我们考虑了一个半线性假抛物方程和一个半线性波方程。

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

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.