论抛物方程控制函数的极值和估计问题

IF 0.2 Q4 MATHEMATICS Moscow University Mathematics Bulletin Pub Date : 2024-05-13 DOI:10.3103/s0027132224700050

I. V. Astashova, D. A. Lashin, A. V. Filinovskiy

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引用次数: 0

摘要

摘要我们考虑了一个与温度控制数学模型相关的极值问题。它基于一般形式的一维非自交抛物方程。将最优控制确定为加权二次函数的最小化函数，我们证明了控制函数和加权函数双重最小值问题解的存在性。我们还获得了以函数值为单位的控制函数规范的上估计值。这些估计值用于证明无界控制函数集的最小化函数的存在性。

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On Problems of Extremum and Estimates of Control Function for Parabolic Equation

Abstract

We consider an extremum problem associated with a mathematical model of the temperature control. It is based on a one-dimensional non-self-adjoint parabolic equation of general form. Determining the optimal control as a function minimizing the weighted quadratic functional, we prove the existence of a solution to the problem of the double minimum by control and weight functions. We also obtain upper estimates for the norm of the control function in terms of the value of the functional. These estimates are used to prove the existence of the minimizing function for unbounded sets of control functions.

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来源期刊

Moscow University Mathematics Bulletin MATHEMATICS-

CiteScore

0.60

自引率

25.00%

发文量

期刊介绍： Moscow University Mathematics Bulletin is the journal of scientific publications reflecting the most important areas of mathematical studies at Lomonosov Moscow State University. The journal covers research in theory of functions, functional analysis, algebra, geometry, topology, ordinary and partial differential equations, probability theory, stochastic processes, mathematical statistics, optimal control, number theory, mathematical logic, theory of algorithms, discrete mathematics and computational mathematics.