Abstract
I. A few problems of the search for an optimal domain can be formulated as follows. Let Ω be an open bounded set of <inline>1</inline> (N = 2 or 3 in general).
This article is a translation of an article originally written in French entitled Problèmes de contrôle des coefficients dans des équations aux dérivées partielles, published in Control Theory, Numerical Methods and Computer Systems Modelling (Proceedings IRIA 1974), A. Bensoussan and J.-L. Lions, eds., Lecture Notes in Economics and Mathematical Systems, 107, Springer-Verlag, (1975), 420–426. The original article was signed only by L. Tartar who delivered the lecture in which he presented joint work that we were performing at that time. We prefer to present its English translation with our both names.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D. Chenais, Un résultat d’existence dans un problème d’identification de domaine, C. R. Acad. Sci. Paris Série A, 276 (1973), 547–550.
D. Chenais, On the existence of a solution in a domain identification problem, J. Math. Anal. Appl. 52 (1975), 189–219.
F. Murat, Un contre-exemple pour le problème du contrôle dans les coefficients, C. R. Acad. Sci. Paris Série A, 273 (1971), 708–711.
F. Murat, Théorèmes de non-existence pour des problèmes de contrôle dans les coefficients, C. R. Acad. Sci. Paris Série A, 274 (1972), 395–398.
F. Murat, Contre-exemples pour divers problèmes où le contrôle intervient dans les coefficients, Ann. Mat. Pura Appl. 12 (1977), 49–68.
S. Spagnolo, Sul limite delle soluzioni di problemi de Cauchy relativi all’equazione del calore, Ann. Sc. Norm. Sup. Pisa 21 (1967), 657–699.
S. Spagnolo, Sulla convergenza di soluzioni di equazioni paraboliche ed ellitiche, Ann. Sc. Norm. Sup. Pisa 22 (1968), 571–597.
A. Marino and S. Spagnolo, Un tipo di approssimazione dell’operatore \( \sum {\;{D_i}({a_{{ij}}}{D_j})} \) con operatori \( \sum {\;{D_i}{{(\beta {D_i})}_x}} \), Ann. Sc. Norm. Sup. Pisa 23 (1969), 657–673.
E. De Giorgi and S. Spagnolo, Sulla convergenza degli integrali dell’energia per operatori ellitici del secondo ordine, Boll. Unione Mat. Ital. 8 (1973), 391–411.
F. Murat and L. Tartar, to appear.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Murat, F., Tartar, L. (1997). On the Control of Coefficients in Partial Differential Equations. In: Cherkaev, A., Kohn, R. (eds) Topics in the Mathematical Modelling of Composite Materials. Progress in Nonlinear Differential Equations and Their Applications, vol 31. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-2032-9_1
Download citation
DOI: https://doi.org/10.1007/978-1-4612-2032-9_1
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7390-5
Online ISBN: 978-1-4612-2032-9
eBook Packages: Springer Book Archive