ON SHAPE STABILITY OF DIRICHLET OPTIMAL CONTROL PROBLEMS IN COEFFICIENTS FOR NONLINEAR ELLIPTIC EQUATIONS

被引：0

作者：

D'Apice, Ciro ^{[1
]}

De Maio, Umberto ^{[2
]}

Kogut, OL'Ga P. ^{[3
,4
]}

机构：

[1] Univ Salerno, Dipartimento Ingn Informaz & Matemat Applicata, I-84084 Fisciano, SA, Italy

[2] Univ Naples Federico II, Dipartimento Matemat & Applicazioni R Caccioppoli, I-80126 Naples, Italy

[3] Natl Acad Sci, Inst Appl Syst Anal, UA-03056 Kiev, Ukraine

[4] Minist Educ & Sci Ukraine, IPSA, UA-03056 Kiev, Ukraine

来源：

ADVANCES IN DIFFERENTIAL EQUATIONS | 2010年 / 15卷 / 7-8期

关键词：

OPTIMIZATION;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study a classical Dirichlet optimal control problem for a nonlinear elliptic equation with the coefficients as controls in L-infinity(Omega). Since such problems have no solutions in general, we make an assumption on the coefficients of the state equation and introduce the class of so-called solenoidal controls. Using the direct method in the calculus of variations, we prove the existence of at least one optimal pair. We also study the stability of the above optimal control problem with respect to the domain perturbation. With this goal we introduce the concept of Mosco-stability for such problems and analyze the variational properties of Mosco-stable problems with respect to different types of domain perturbations.

引用

页码：689 / 720

页数：32

共 50 条

[31] PROBLEMS OF OPTIMAL-CONTROL FOR LINEAR ELLIPTIC EQUATIONS
RAITUM, UE
DOKLADY AKADEMII NAUK SSSR, 1979, 244 (04): : 828 - 830
[32] Optimization Problems with Gradient of Control's in the Coefficients of Elliptic Equations
A. D. Iskenderov
R. A. Gamidov
Automation and Remote Control, 2020, 81 : 1627 - 1636
[33] Optimization Problems with Gradient of Control's in the Coefficients of Elliptic Equations
Iskenderov, A. D.
Gamidov, R. A.
AUTOMATION AND REMOTE CONTROL, 2020, 81 (09) : 1627 - 1636
[34] Approximations of optimal control problems for semilinear elliptic equations with discontinuous coefficients and solutions and with control in matching boundary conditions
F. V. Lubyshev
A. R. Manapova
M. E. Fairuzov
Computational Mathematics and Mathematical Physics, 2014, 54 : 1700 - 1724
[35] Approximations of optimal control problems for semilinear elliptic equations with discontinuous coefficients and solutions and with control in matching boundary conditions
Lubyshev, F. V.
Manapova, A. R.
Fairuzov, M. E.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2014, 54 (11) : 1700 - 1724
[36] Approximations of optimal control problems for semilinear elliptic equations with discontinuous coefficients and states and with controls in the coefficients multiplying the highest derivatives
F. V. Lubyshev
M. E. Fairuzov
Computational Mathematics and Mathematical Physics, 2016, 56 : 1238 - 1263
[37] Approximations of optimal control problems for semilinear elliptic equations with discontinuous coefficients and states and with controls in the coefficients multiplying the highest derivatives
Lubyshev, F. V.
Fairuzov, M. E.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2016, 56 (07) : 1238 - 1263
[38] Extrapolation of the Dirichlet problem for elliptic equations with complex coefficients
Dindos, Martin
Pipher, Jill
JOURNAL OF FUNCTIONAL ANALYSIS, 2020, 279 (07)
[39] THE DIRICHLET PROBLEM FOR NONLINEAR DEGENERATE ELLIPTIC EQUATIONS
王传芳
ScienceBulletin, 1985, (03) : 422 - 423
[40] The Dirichlet to Neumann Operator for Nonlinear Elliptic Equations
Ly, Ibrahim
Tarkhanov, Nikolai
COMPLEX ANALYSIS AND DYNAMICAL SYSTEMS IV, PT 2: GENERAL RELATIVITY, GEOMETRY, AND PDE, 2011, 554 : 115 - 126

← 1 2 3 4 5 →