On Computing the Gradient in a Control Problem for a Higher-Order Pseudoparabolic Equation

IF 0.8 4区数学 Q3 MATHEMATICS

Doklady Mathematics Pub Date : 2026-07-05 DOI:10.1134/S106456242670002X

A. M. Romanenkov

引用次数: 0

Abstract

A control problem is considered for the solution to an initial-boundary value problem for a linear differential equation of pseudoparabolic type that is higher-order in the spatial variable. The existence of a generalized solution is studied, and a constructive approach to constructing this solution using the Galerkin method is proposed. The control problem is stated for an integral quadratic functional, for which a majorant functional is constructed. For the introduced functional, the gradient is explicitly computed, making it possible to use the gradient descent method for computations.

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高阶伪抛物方程控制问题中梯度的计算

考虑了空间变量高阶伪抛物型线性微分方程初边值问题的控制问题。研究了一个广义解的存在性，并给出了用伽辽金方法构造该解的构造方法。研究了一类积分二次泛函的控制问题，并构造了一个主泛函。对于引入的泛函，可以显式地计算梯度，从而可以使用梯度下降法进行计算。

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

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 It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications.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.