Locally adjoint mappings and optimization of the first boundary value problem for hyperbolic type discrete and differential inclusions

E. N. Mahmudov

doi:10.1016/j.na.2006.09.054

Locally adjoint mappings and optimization of the first boundary value problem for hyperbolic type discrete and differential inclusions

E. N. Mahmudov^*

^*Corresponding author for this work

Department of Mathematics Engineering

Research output: Contribution to journal › Article › peer-review

43 Citations (Scopus)

Abstract

The present paper deals with discrete approximation on a uniform grid of the first boundary value problem (P_C) for differential inclusions of hyperbolic type. In the form of Euler-Lagrange inclusions, necessary and sufficient conditions for optimality are derived for the discrete (P_D) and continuous (P_C) problems on the basis of new concepts of locally adjoint mappings. The results obtained are generalized to the multidimensional case with a second order elliptic operator.

Original language	English
Pages (from-to)	2966-2981
Number of pages	16
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	67
Issue number	10
DOIs	https://doi.org/10.1016/j.na.2006.09.054
Publication status	Published - 15 Nov 2007

Keywords

Boundary value problems
Discrete and differential inclusion
Discrete approximation
Locally adjoint mappings
Necessary and sufficient conditions
Nonsmooth analysis

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10.1016/j.na.2006.09.054

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abstract = "The present paper deals with discrete approximation on a uniform grid of the first boundary value problem (PC) for differential inclusions of hyperbolic type. In the form of Euler-Lagrange inclusions, necessary and sufficient conditions for optimality are derived for the discrete (PD) and continuous (PC) problems on the basis of new concepts of locally adjoint mappings. The results obtained are generalized to the multidimensional case with a second order elliptic operator.",

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AB - The present paper deals with discrete approximation on a uniform grid of the first boundary value problem (PC) for differential inclusions of hyperbolic type. In the form of Euler-Lagrange inclusions, necessary and sufficient conditions for optimality are derived for the discrete (PD) and continuous (PC) problems on the basis of new concepts of locally adjoint mappings. The results obtained are generalized to the multidimensional case with a second order elliptic operator.

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KW - Discrete and differential inclusion

KW - Discrete approximation

KW - Locally adjoint mappings

KW - Necessary and sufficient conditions

KW - Nonsmooth analysis

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Locally adjoint mappings and optimization of the first boundary value problem for hyperbolic type discrete and differential inclusions

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Keywords

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