SPECTRAL PROBLEMS ARISING IN THE STABILIZATION PROBLEM FOR THE LOADED HEAT EQUATION: A TWO-DIMENSIONAL AND MULTI-POINT CASES

被引：4

作者：

Jenaliyev, M. T. ^{[1
]}

Imanberdiyev, K. B. ^{[1
,2
]}

Kassymbekova, A. S. ^{[2
]}

Sharipov, K. S. ^{[3
]}

机构：

[1] Inst Math & Math Modeling, Pushkin Str 125, Alma Ata 050010, Kazakhstan

[2] Al Farabi Kazakh Natl Univ, Al Farabi Ave 71, Alma Ata 050040, Kazakhstan

[3] Kazakh Univ Ways Commun, Zhetysu 1 Mcr,B-32a, Alma Ata 050063, Kazakhstan

来源：

EURASIAN JOURNAL OF MATHEMATICAL AND COMPUTER APPLICATIONS | 2019年 / 7卷 / 01期

关键词：

boundary stabilization; heat equation; spectrum; loaded Laplace operator;

D O I：

10.32523/2306-6172-2019-7-1-23-37

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Spectral properties of a loaded two-dimensional Laplace operator, studied in this work are the application with the stabilization of solutions of problems for the heat equation. The stabilization problem (of forming a cylinder) of a solution of boundary value problem for heat equation with the loaded two-dimensional Laplace operator is considered. An algorithm is proposed for approximate construction of boundary controls providing the required stabilization of the solution. The work continues the research of the authors carried out earlier for the loaded one-dimensional heat equation. The idea of reducing the stabilization problem for a parabolic equation by means of boundary controls to the solution of an auxiliary boundary value problem in the extended domain of independent variables belongs to A.V. Fursikov. At the same time, recently, the so-called loaded differential equations are actively used in problems of mathematical modeling and control of nonlocal dynamical systems.

引用

页码：23 / 37

页数：15

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