Abstract
We study the simulation and the control of a Stefan problem with heat source along the free boundary. Such a problem can be associated with the continuous casting process taking the convection in the liquid into account. The initial problem is transformed into a variational inequality (V.I) in which the free boundary appears explicitly in the second member. We prove the existence of a solution of this V.I and we study some associated optimal control problems. Numerical methods are presented.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
C. Baiocchi: Problèmes à frontière libre et inéquations variationnelles (C.R.A.S. t. 283, 12 Juillet 1976).
A. Friedman, D. Kinderlehrer: A class of parabolic variational inequalities (J. of Diff. Eq. 21, 1976).
R. Glowinski, J.L. Lions, R. Trémolières: Analyse numérique des inéquations variationnelles (Dunod, 1976).
M. Larrecq, C. Saguez: Modèle mathématique de la solidification en coulée continue tenant compte de la convection à l'interface liquidesolide (Journées Métallurgiques d'Automne, 1977).
F. Mignot: Contrôle dans les inéquations variationnelles elliptiques (Thesis, Paris VI, 1975).
C. Saguez: Un problème de Stefan avec source sur la frontière libre (Rapport Laboria, 1977).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1978 Springer-Verlag
About this paper
Cite this paper
Saguez, C. (1978). A variational inequality associated with a Stefan problem simulation and control. In: Stoer, J. (eds) Optimization Techniques Part 1. Lecture Notes in Control and Information Sciences, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007254
Download citation
DOI: https://doi.org/10.1007/BFb0007254
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08707-6
Online ISBN: 978-3-540-35891-6
eBook Packages: Springer Book Archive