Optimal control of an elliptic equation with a nonsmooth nonlinearity
type: Item
instance of: scholarly article
title: Optimal control of an elliptic equation with a nonsmooth nonlinearity
zbMATH Open document ID: 1084.49024
published in: Differential Equations
publication date: 2005-06-17T00:00:00Z
review text: The paper considers the problem of minimizing a quadratic functional on pairs \((y, u)\), which satisfy the elliptic equation \(\Delta y- g(y)= u+ f\) with the nondifferentiable function \(g\). Under assumptions of monotonicity of \(g\) the author approximates \(g\) by smooth functions, derives the optimality system for the approximate problem and shows the convergence of the corresponding costs of the approximate problems to the cost of the original problem.
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 35B37
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 2176609
zbMATH Keywords: optimal control
zbMATH Keywords: elliptic equation
zbMATH Keywords: approximation of nonsmooth nonlinearity
Wikidata QID: Q115335073
author: S. Ya. Serovaiskii
reviewed by: Uldis Raitums
MaRDI profile type: Publication
full work available at URL: b:dieq.0000017922.16111.2f
OpenAlex ID: W2070311336
DOI: 10.1023/B:DIEQ.0000017922.16111.2F
description: scientific article; zbMATH DE number 2176609