Boundary control for the heat equation with nonlinear boundary condition
type: Item
instance of: scholarly article
title: Boundary control for the heat equation with nonlinear boundary condition
zbMATH Open document ID: 0679.49002
DOI: 10.1016/0022-0396(89)90077-6
author: E. J. P. Georg Schmidt
published in: Journal of Differential Equations
publication date: 1989-01-01T00:00:00Z
review text: This paper treats boundary control of the heat equation subject to a boundary condition which prescribes the normal derivative of the surface temperature as a function of the surface temperature and the ambient temperature, the latter being treated as the control. The existence and uniqueness of weak solutions is established; this permits one to prove the existence of optimal solutions to certain approximation problems. Finally a ``bang-bang'' principle is proved for a problem in 1 space dimension. This depends in a delicate way on unique backwards continuation as well as on results concerning strict total positivity and the heat equation due to the author [ibid. 62, 275--298 (1986; Zbl 0549.35052)].
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 49J30
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 80A19
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 4113361
zbMATH Keywords: bang-bang principle
zbMATH Keywords: nonlinear boundary condition
zbMATH Keywords: boundary control
zbMATH Keywords: heat equation
zbMATH Keywords: strict total positivity
reviewed by: Tamás Schmidt
MaRDI profile type: Publication
full work available at URL: 0022-0396(89)90077-6
OpenAlex ID: W2036414777
cites work: Boundary Control Problems with Nonlinear State Equation
cites work: Conduction of heat in solids
cites work: Q5612126
cites work: Q5520962
cites work: Q3284078
cites work: Q4040640
cites work: Restricted approximation by strongly sign-regular kernels: The finite bang-bang principle
cites work: Boundary Control of Parabolic Differential Equations in Arbitrary Dimensions: Supremum-Norm Problems
cites work: Q5643065
cites work: The problem of the number of switches in parabolic equations with control
cites work: Q5562267
cites work: Unicité du prolongement des solutions pour quelques opérateurs différentiels paraboliques
cites work: Q3094428
cites work: A Parabolic Control Problem with a Boundary Condition of the Stefan‐Boltzmann Type
cites work: Q4159882
cites work: Q4189718
cites work: Boundary Control for the Heat Equation with Steady-State Targets
cites work: On the total - and strict total - positivity of the kernels associated with parabolic initial boundary value problems
cites work: On the Boundary Behavior of Solutions to Elliptic and Parabolic Equations—with Applications to Boundary Control for Parabolic Equations
cites work: Optimale Steuerung einer Klasse nichtlinearer Aufheizungsprozesse
description: scientific article; zbMATH DE number 4113361