半线性椭圆对流-扩散方程的近似最优控制问题与边界观测的共形衍射，以及对流传输算子系数和方程非线性项的控制

IF 0.7 4区数学 Q3 MATHEMATICS, APPLIED

Computational Mathematics and Mathematical Physics Pub Date : 2024-09-01 DOI:10.1134/s0965542524700659

F. V. Lubyshev, M. E. Fairuzov

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引用次数: 0

摘要

摘要我们研究了一个最优控制问题的差分近似，该问题的边界观测是半线性椭圆方程的 Dirichlet 问题所描述的状态的常导数，其控制涉及对流传输算子的系数和方程的非线性项。研究了最优控制问题的好求性。构建了最优控制问题的差分近似值。分析了近似值对函数和控制的收敛性。构建了近似值的正则化。

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Approximation of Optimal Control Problems for Semilinear Elliptic Convection–Diffusion Equations with Boundary Observation of the Conormal Derivative and with Controls in Coefficients of the Convective Transport Operator and in Nonlinear Term of the Equation

Abstract

We study difference approximations of an optimal control problem with a boundary observation of the conormal derivative of the state described by the Dirichlet problem for semilinear elliptic equations with controls involved in coefficients of the convective transport operator and in the nonlinear term of the equation. The well-posedness of the optimal control problem is examined. Difference approximations for the optimal control problem are constructed. The convergence of the approximations with respect to the functional and control is analyzed. A regularization of the approximations is constructed.

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来源期刊

Computational Mathematics and Mathematical Physics MATHEMATICS, APPLIED-PHYSICS, MATHEMATICAL

CiteScore

1.50

自引率

14.30%

发文量

125

审稿时长

4-8 weeks

期刊介绍： Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.