Convergence of Distributed Optimal Controls on the Internal Energy in Mixed Elliptic Problems when the Heat Transfer Coefficient Goes to Infinity

We consider a steady-state heat conduction problem P

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Published in:Applied mathematics & optimization 2003-05, Vol.47 (3), p.213-230
Main Authors: Gariboldi, Claudia M., Tarzia, Domingo A.
Format: Article
Language:English
Subjects:
BOUNDARY CONDITIONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CONVERGENCE
Energy
FUNCTIONS
Heat transfer
Inequality
MATHEMATICAL SPACE
OPTIMAL CONTROL
POISSON EQUATION
STEADY-STATE CONDITIONS
THERMAL CONDUCTION
VARIATIONAL METHODS
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container_title Applied mathematics & optimization
container_volume 47
creator Gariboldi, Claudia M.
Tarzia, Domingo A.
description We consider a steady-state heat conduction problem P
doi_str_mv 10.1007/s00245-003-0761-y
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We formulate distributed optimal control problems over the internal energy <g< for each <[alpha]< . We prove that the optimal control < g_ op<<<[alpha] <<< < and its corresponding system <u_ g_ op<<<[alpha] <<< [alpha] < and adjoint <p_ g_ op<<<[alpha] <<< [alpha] < states for each <[alpha] < are strongly convergent to <g<<<op<<<,< <u_ g<<<op<<< < and < p _ g<<<op<<< < , respectively, in adequate functional spaces. We also prove that these limit functions are respectively the optimal control, and the system and adjoint states corresponding to another distributed optimal control problem for the same Poisson equation with a different boundary condition on the portion <[Gamma]<<<1<< . 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We formulate distributed optimal control problems over the internal energy <g< for each <[alpha]< . We prove that the optimal control < g_ op<<<[alpha] <<< < and its corresponding system <u_ g_ op<<<[alpha] <<< [alpha] < and adjoint <p_ g_ op<<<[alpha] <<< [alpha] < states for each <[alpha] < are strongly convergent to <g<<<op<<<,< <u_ g<<<op<<< < and < p _ g<<<op<<< < , respectively, in adequate functional spaces. We also prove that these limit functions are respectively the optimal control, and the system and adjoint states corresponding to another distributed optimal control problem for the same Poisson equation with a different boundary condition on the portion <[Gamma]<<<1<< . 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subjects BOUNDARY CONDITIONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CONVERGENCE
Energy
FUNCTIONS
Heat transfer
Inequality
MATHEMATICAL SPACE
OPTIMAL CONTROL
POISSON EQUATION
STEADY-STATE CONDITIONS
THERMAL CONDUCTION
VARIATIONAL METHODS
title Convergence of Distributed Optimal Controls on the Internal Energy in Mixed Elliptic Problems when the Heat Transfer Coefficient Goes to Infinity
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