Optimal control of nonsmooth system governed by quasi-linear elliptic equations
type: Item
instance of: scholarly article
title: Optimal control of nonsmooth system governed by quasi-linear elliptic equations
zbMATH Open document ID: 0894.49015
DOI: 10.1155/S0161171297000458
author: Liutang Gong
author: Pusheng Fei
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1998-08-18T00:00:00Z
full work available at URL: https://eudml.org/doc/47936
review text: The authors have discussed the following optimal control problem: \[ \min _{u\in L^2(\Omega)}G(y)+\Phi (u), \] where \(y\) is the solution of \[ -\sum _{i=1}^n(a_i(y_{x_i}))_{x_i}=u \quad \text{in }\Omega, \qquad y=0\quad \text{on }\partial \Omega . \] Here \(G\) is a lower semicontinuous convex function and \(\Phi \) is a convex function. Through the smoothness and the approximation of the initial problem the necessary condition has been obtained. This can be considered as the Euler-Lagrange condition in the quasi-linear case.
reviewed by: Sebastian Aniţa
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 1046343
zbMATH Keywords: optimal control
zbMATH Keywords: quasi-linear equation
zbMATH Keywords: necessary optimality condition
MaRDI profile type: Publication
OpenAlex ID: W2110229821
description: scientific article; zbMATH DE number 1046343