二维Boussinesq方程的最优起动控制问题

IF 0.8 3区数学 Q2 MATHEMATICS

Izvestiya Mathematics Pub Date : 2022-01-01 DOI:10.1070/IM9099

E. Baranovskii

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引用次数: 0

摘要

研究粘性流体非等温流动的二维Boussinesq方程的最优启动控制问题。通过对可容许元组和演化算子性质的研究，证明了在模型数据的自然假设下优化问题的可解性。我们导出了一个变分不等式，当目标函数由最终观测值确定时，最优控制满足该变分不等式。得到了最优控制的唯一性的充分条件。

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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The optimal start control problem for 2D Boussinesq equations

We consider the problem of the optimal start control for two-dimensional Boussinesq equations describing non-isothermal flows of a viscous fluid in a bounded domain. Using the study of the properties of admissible tuples and of the evolution operator, we prove the solubility of the optimization problem under natural assumptions about the model data. We derive a variational inequality which is satisfied by the optimal control provided that the objective functional is determined by the final observation. We also obtain sufficient conditions for the uniqueness of an optimal control.

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来源期刊

Izvestiya Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. This publication covers all fields of mathematics, but special attention is given to: Algebra; Mathematical logic; Number theory; Mathematical analysis; Geometry; Topology; Differential equations.