不连续非线性Sturm - Liouville问题的控制与摄动

IF 0.3 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya Pub Date : 2023-01-01 DOI:10.21638/11701/spbu10.2023.212

O. Baskov, D. Potapov

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引用次数: 0

摘要

考虑具有不连续非线性、控制和摄动的Sturm - Liouville问题。将已有的具有谱参数和不连续算子的方程的结果应用于该问题。利用变分方法，我们建立了不连续非线性Sturm - Liouville问题解的存在性定理和最优控制问题解的存在性定理，以及可接受的“控制状态”对集合的拓扑性质。作为一个应用，给出了不可压缩流体的控制和扰动分离流动的Gol’shtik模型的一维模拟。

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Control and perturbation in Sturm — Liouville’s problem with discontinuous nonlinearity

We consider the Sturm — Liouville problem with discontinuous nonlinearity, control and perturbation. Previously obtained results for equations with a spectral parameter and a discontinuous operator are applied to this problem. By the variational method, we have established theorems on the existence of solutions to the Sturm — Liouville problem with discontinuous nonlinearity and to the optimal control problem, as well as on topological properties of the set of the acceptable “control — state” pairs. A one-dimensional analog of the Gol’dshtik model for separated flows of an incompressible fluid with control and perturbation is given as an application.

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来源期刊

Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

1.30

自引率

50.00%

发文量

期刊介绍： The journal is the prime outlet for the findings of scientists from the Faculty of applied mathematics and control processes of St. Petersburg State University. It publishes original contributions in all areas of applied mathematics, computer science and control. Vestnik St. Petersburg University: Applied Mathematics. Computer Science. Control Processes features articles that cover the major areas of applied mathematics, computer science and control.