On approximation of an optimal boundary control problem for linear elliptic equation with unbounded coefficients

Kogut, Peter I.

doi:10.3934/dcds.2014.34.2105

Cited by 24 publications

(18 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By the initial assumptions, we have h ∈ L(A). Then the condition (iii) of Definition 3.1 implies that (for the details we refer to [11])…”

Section: Proof Since Each Of the Optimization Problems Infmentioning

confidence: 99%

Optimal $L^2$-control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions

Horsin¹,

Kogut²,

Wilk³

2016

MCRF

View full text Add to dashboard Cite

In this paper we study we study a Dirichlet optimal control problem associated with a linear elliptic equation the coefficients of which we take as controls in the class of integrable functions. The characteristic feature of this control object is the fact that the skew-symmetric part of matrix-valued control A(x) belongs to L 2 -space (rather than L ∞ ). In spite of the fact that the equations of this type can exhibit non-uniqueness of weak solutions, the corresponding OCP, under rather general assumptions on the class of admissible controls, is well-posed and admits a nonempty set of solutions [9]. However, the optimal solutions to such problem may have a singular character. We show that some of optimal solutions can be attainable by solutions of special optimal control problems in perforated domains with fictitious boundary controls on the holes.

show abstract

“…By the initial assumptions, we have h ∈ L(A). Then the condition (iii) of Definition 3.1 implies that (for the details we refer to [11])…”

Section: Proof Since Each Of the Optimization Problems Infmentioning

confidence: 99%

Optimal $L^2$-control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions

Horsin¹,

Kogut²,

Wilk³

2016

MCRF

View full text Add to dashboard Cite

show abstract

“…Several results for optimal control problems related to elliptic PDE's with unbounded coefficients have been also obtained in [26,21,22,27,28,9,10] and the recent papers [20], [30] with the reference therein).…”

mentioning

confidence: 91%

An optimal control problem for some nonlinear elliptic equations with unbounded coefficients

Zecca¹

2019

Discrete &Amp; Continuous Dynamical Systems - B

View full text Add to dashboard Cite

“…Using the direct method of the Calculus of Variations, we show in Section 4 that the optimal control problem (1)-(4) has a nonempty set of solutions provided the admissible controls A(x) are uniformly bounded in BV -norm, in spite of the fact that the corresponding quasilinear differential operator −div |(A∇y, ∇y) R N | p−2 2 A∇y , in principle, has degeneracies as |A 1 2 ∇y| tends to zero [1]. Moreover, when the term |(A∇y, ∇y) R N | p− 2 2 is regarded as the coefficient of the Laplace operator, we have the case of unbounded coefficients (see [12,14]). In order to avoid degeneracy with respect to the control A(x), we assume that matrix A(x) has a uniformly bounded spectrum away from zero.…”

Section: Introductionmentioning

confidence: 99%

On attainability of optimal controls in coefficients for system of Hammerstein type with anisotropic p-Laplacian

2016

View full text Add to dashboard Cite

In this paper we consider an optimal control\ud problem (OCP) for the coupled system of a nonlinear monotone Dirichlet problem with anisotropic p-Laplacian and matrix-valued L^infinity(Omega, R^(NxN))-controls in its coefficients\ud and a nonlinear equation of Hammerstein type. Using the direct\ud method in calculus of variations, we prove the existence of an optimal control in considered problem and provide sensitivity analysis for a specific case of considered problem with respect to two-parameter regularization

show abstract

On approximation of an optimal boundary control problem for linear elliptic equation with unbounded coefficients

Cited by 24 publications

References 11 publications

Optimal $L^2$-control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions

Optimal $L^2$-control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions

An optimal control problem for some nonlinear elliptic equations with unbounded coefficients

On attainability of optimal controls in coefficients for system of Hammerstein type with anisotropic p-Laplacian

Contact Info

Product

Resources

About