Semidiscrete Ritz-Galerkin approximation of nonlinear parabolic boundary control problems -- strong convergence of optimal controls
type: Item
instance of: scholarly article
title: Semidiscrete Ritz-Galerkin approximation of nonlinear parabolic boundary control problems -- strong convergence of optimal controls
zbMATH Open document ID: 0802.49017
DOI: 10.1007/BF01189480
published in: Applied Mathematics and Optimization
publication date: 1994-05-05T00:00:00Z
review text: The paper discusses an optimal control problem for the linear parabolic equation \(y_ t= \Delta y-y\) with nonlinear Neumann type boundary conditions \(\partial y/\partial n= b(t,x,y,u)\). Controls \(u\) belong to a standard convex set. Additional constraints are of the form of inequalities for integrals over the spatial domain. Under some regularity assumptions and the assumption that the second derivative of the Lagrange function with respect to the state and controls is strongly positive at the local minimum \((y_ 0, u_ 0)\), the author proves that the solutions of Ritz-Galerkin semidiscrete approximations strongly converges to \((y_ 0, u_ 0)\).
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 65M60
zbMATH DE Number: 563451
zbMATH Keywords: linear parabolic equation
zbMATH Keywords: Ritz-Galerkin semidiscrete approximations
author: Fredi Tröltzsch
reviewed by: Uldis Raitums
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01189480
OpenAlex ID: W144579591
description: scientific article; zbMATH DE number 563451