高阶双曲型方程控制问题中极大值原理形式的最优性准则

IF 0.8 4区数学 Q3 MATHEMATICS

Doklady Mathematics Pub Date : 2026-09-04 DOI:10.1134/S1064562426700092

M. B. Bulakina, A. M. Romanenkov

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引用次数: 0

摘要

研究了一类高阶线性伪双曲型方程的最优控制问题，该方程的右侧控制只依赖于时间。这个方程被简化为两个偏微分方程的系统。用针变分法以庞特里亚金极大值原理的形式得到了必要的最优性条件。建立了弱解的唯一性。

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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Optimality Criterion in the Form of Maximum Principle in Control Problems for High-Order Hyperbolic Equations

An optimal control problem for a high-order linear pseudohyperbolic equation with a right-hand side control dependent only on time is considered. The equation is reduced to a system of two partial differential equations. The needle variation method is used to obtain necessary optimality conditions in the form of Pontryagin’s maximum principle. The uniqueness of a weak solution is established.

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来源期刊

Doklady Mathematics 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3-6 weeks

期刊介绍： Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.