退化椭圆型方程边值问题的最优控制

Q3 Mathematics Matematychni Studii Pub Date : 2023-03-28 DOI:10.30970/ms.59.1.76-85
I. Pukal’skii, B. Yashan
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引用次数: 0

摘要

研究了用二阶椭圆方程的斜导数问题描述的系统最优控制问题。考虑内部和边界管理的情况。质量判据由体积积分与表面积分之和给出。方程的系数和边界条件允许任意变量在某一组点处具有任意阶的幂奇点。研究了具有光滑系数的辅助问题的解。利用先验估计,建立了在特殊H\{0}空间中求解问题及其导数的不等式。利用Archel和Riess定理,将收敛序列与辅助问题的紧致解序列区分开来,紧致解序列的极限值就是给定问题的解。建立了一类带简并椭圆型方程边值问题所描述的系统最优解存在的充分必要条件。
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Optimal control in the boundary value problem for elliptic equations with degeneration
The problem of optimal control of the system described by the oblique derivative problem forthe elliptic equation of the second order is studied. Cases of internal and boundary managementare considered. The quality criterion is given by the sum of volume and surface integrals.The coefficients of the equation and the boundary condition allow power singularities of arbitraryorder in any variables at some set of points. Solutions of auxiliary problems with smooth coefficients are studied to solve the given problem. Using a priori estimates, inequalities are established for solving problems and their derivatives in special H\"{o}lder spaces. Using the theorems of Archel and Riess, a convergent sequence is distinguished from a compact sequence of solutions to auxiliary problems, the limiting value of which will bethe solution to the given problem. The necessary and sufficient conditions for the existence of the optimal solution of the systemdescribed by the boundary value problem for the elliptic equation with degeneracy have been established.
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Matematychni Studii
Matematychni Studii Mathematics-Mathematics (all)
CiteScore
1.00
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0.00%
发文量
38
期刊介绍: Journal is devoted to research in all fields of mathematics.
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