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

Mahmudov E.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, vol.67, no.10, pp.2966-2981, 2007 (SCI-Expanded) identifier identifier


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 (P-D) 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. (C) 2007 Published by Elsevier Ltd.