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 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 67 Issue: 10
  • Publication Date: 2007
  • Doi Number: 10.1016/j.na.2006.09.054
  • Title of Journal : NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
  • Page Numbers: pp.2966-2981

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 (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.