Champs d'intérêt et thèmes d'enseignement
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| Le spectre des intérêts et activités va des questions d'analyse
mathématique aux applications réelles aux problèmes provenant des sciences de
l'ingénieur. Les travaux initiaux ont porté sur les aspects fondamentaux de la
théorie et du contrôle des sytèmes à retard. En parallèle quelques
travaux sur la théorie des jeux pour les systèmes économiques et la gestion des
soins infirmiers. Le contrôle des systèmes de dimension infinie a été la
prolongation du thème des systèmes à retard. Il a débouché sur le
contrôle des structures flexibles avec ses application aux problèmes
aérospatiaux. Un nouveau cadre fonctionnel a été créé pour la
résolution numériques des équations différentielles ordinaires par des
méthodes de splines discontinus. Ceci a permis de retrouver toutes les bonnes
méthodes à un pas et à multipas et de construire des familles entières de
schémas d'approximation des équations nonlinéaires matricielles de Riccati et
à l'étude de l'ordre de l'erreur d'approximation. Plus récemment l'attention
s'est déplacée vers les problèmes de santé dans le cadre de l'Organisation
Mondiale de la Santé pour le problème des épandages insecticides dans les
rivières d'Africe occidentale pour combattre l'Onchocercose. Mais l'effort le plus
important des dernières années porte sur les problèmes et les mathématiques
de l'analyse et de l'optimisation géométrique de forme et de structure. Bien que
l'objectif soit assez précis, c'est un domaine mathématiquement très vaste car
il fait appel à la théorie moderne des équations aux dérivées
partielles, l'optimisation, l'analyse numérique et la théorie géométrique
de la mesure. Les défits sont importants tant pour la formulation des problème, le
choix et la création des outils mathématiques que pour la conception et la mise en
oeuvre d'algorithmes efficaces et naturellement adaptés à ces problèmes. Enfin
depuis plusieurs années il existe toujours une activité constante sur les
problèmes de distribution des fréquences radio dans les grands centres urbains
canadiens.
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Publications
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Articles avec comité de lecture
- M.C. DELFOUR, Characterization of the space of the membrane shell equation for
arbitrary C^{1,1) midsurfaces}, Control and Cybernetics 28 (3) (1999), pp 481-501. (21
pages)
- M.C. DELFOUR et F. DUBEAU, Fixed mesh approximation of ordinary differential equations
with impulses, Numerisch Mathematics 78 (1998), 377-401. (25 pages)
- G. YANG, M.C. DELFOUR and M. FORTIN, Uniformly convergent mixed finite elements for
cylindrical shells, Advances in Computational Mathematics 7 (1997) 3, pp. 261-277 (13
pages).
- M.C. DELFOUR et J. P. ZOLESIO, Tangential Differential Equations for Dynamical
Thin/Shallow Shells, J. Differential Equations 128 (1996), 125-167 (43 pages). (Academic
Press, New York, London)
- M.C. DELFOUR and J.P. ZOLESIO, On the design and control of systems governed by
differential equations on bubmanifolds, Control and Cybernetics 25 (1996), 497--514. (18
pages)
- M.C. DELFOUR et J. P. ZOLESIO, A boundary differential equation for thin shells, J.
Differential Equations 119 (1995), 426--449 (24 pages) (Academic Press, New York,
London)
- M.C. DELFOUR et J. MORGAN, One-sided derivative of MinMax and saddle points with
respect to a parameter, Optimization, Vol 31 (1994), 343-358 (16 pages)
- M.C. DELFOUR et J. P. ZOLESIO, Shape analysis via oriented distance functions, J.
Functional Analysis, Vol 123 No. 1 (1994) 129-201 (73 pages). (Academic Press, New York,
London)
- M.C. DELFOUR et J. MORGAN, A complement to the differentiability of saddle points and
min max, Optimal Control: Applications and Methods Vol. 13 (1992), 87-94. (8 pages)
- M.C. DELFOUR et A. OUANSAFI, Noniterative approximations to the solution of the matrix
Riccati differential equation, SIAM J. Numerical Analysis Vol. 29, No. 6 (1992), 1-46. (46
pages) (Society for Industrial and Applied Mathematics, Philadelphis, Penn.).
- A. CHALIFOUR et M.C. DELFOUR, Optimal distribution of larvicide in running waters, SIAM
J. on Optimization 2, No. 2 (1992), 264-303. (40 pages) (Society for Industrial and Applied
Mathematics, Philadelphis, Penn.).
- M.C. DELFOUR et J.P. ZOLESIO, Structure of Shape Derivatives for Nonsmooth Domains, J.
Functional Analysis Vol. 104, No. 1 (1992), 1-33. (27 pages) (Academic Press,New York,
London)
- G. DA PRATO and M.C. DELFOUR, Unbounded solutions to the linear quadratic control
problem, SIAM J. on Control and Optim. Vol. 30, No. 1 (1992), pp. 31-48. (18 pages)
(Society for Industrial and Applied Mathematics, Philadelphis, Penn.).
- M.C. DELFOUR and J.P. ZOLESIO, Velocity Method and Lagrangian Formulation for the
Computation of the Shape Hessian, SIAM J. on Control and Optim. 29, No 6 (1991), 1414-1442.
(29 pages) (Society for Industrial and Applied Mathemati25.01.2008omité de lecture
- M.C. DELFOUR and J.P. ZOLESIO, Velocity method and Courant metric topologies in shape
analysis of partial differential equations, dans "Control of Nonlinear Distributed
Parameter Systems", G. Chen, I. Lasiecka and J. Zhou, eds, Marcel Dekker, New York, à
paraître (Confeerence en l'honneur du 60e anniversaire de D.L. Russell, Texas).
- M.C. DELFOUR, Tangential differential calculus and functional analysis on a C^{1,1}
submanifold, in "Differential-geometric methods in the control of partial differential
equations", R. Gulliver, W. Littman and R. Triggiani, eds., Contemporary Mathematics, AMS
Publications, à paraître (Proc. of the conference held in Boulder, Colorado, June
28-July 2, 1999) (34 pages).
- M.C. DELFOUR, Membrane shell equation: characterization of the space of solutions, in
Control of Distributed Parameter and Stochastic Systems, Shuping Chen, Xunjing Li, Jiongmin
Yong, Xun Yu Zhou , eds., pp 21-29, Chapman and Hall New York 1999 (Hangzhou, China juin
1998).
- M.C. DELFOUR, Intrinsic P(2,1 thin shell model and Naghdi's models without a priori
assumption on the stress tensor, in Optimal Control of Partial Differential Equations, K.H.
Hoffmann, G. Leugering, F. Tröltzsch, eds., pp. 99-113, Int. Ser. Of Numererical
Mathematics, Vol. 133, Birkhäuser Verlag, Basel 1999. (Chemnitz, Germany, April 20-24,
1998)
- M.C. DELFOUR and J.P. ZOLESIO, Hidden boundary smoothness in hyperbolic tangential
problems on nonsmooth domains, in "Systems modelling and optimization" (Proceedings of the
18th IFIP Conference on Systems Modelling and Optimization, Detroit, MI, July 1997), pp.
53-61, Res. Notes Math., Vol. 396, Chapman & Hall/CRC, Boca Raton, FL, 1999.
- M.C. DELFOUR and J.P. ZOLESIO, Shape analysis via distance functions: local theory, in
``Boundaries, interfaces and transitions", M. Delfour, ed., pp. 91-123, CRM Proc. Lect.
Notes Ser., AMS Publications, Providence, R.I. 1998. (33 pages) (American Mathematical
Society, Providence, R.I.)
- M.C. DELFOUR, Intrinsic differential geometry methods in the asymptotic analysis of
linear thin shells, in ``Boundaries, interfaces and transitions", M. Delfour, ed., pp.
19-90, CRM Proc. Lect. Notes Ser., AMS Publications, Providence, R.I. 1998. (72 pages)
(American Mathematical Society, Providence, R.I.)
- G. YANG, M.C. DELFOUR and M. FORTIN, Uniform error analysis of mixed finite elements
for cylindrical shells, "Plates and Shells", M. Fortin, ed., pp. 267-280, CRM Proc.Lect.
Notes ser., Vol. 21, AMS Publications, Providence, R.I. 1999 (1996 CMS Annual Seminar) (14
pages)
- M.C. DELFOUR and J. ZHAO, Intrinsic Nonlinear Models of Shells, in "Plates and Shells",
M. Fortin, ed., pp. 109-123, CRM Proc. Lect. Notes ser., Vol. 21, AMS Publications,
Providence, R.I. 1999 (1996 CMS Annual Seminar, Quebec City) (15 pages) (American
Mathematical Society, Providence, R.I.)
- M.C. DELFOUR and J.-P. ZOLESIO, Convergence of the linear P(1,1) and P(2,1) thin shells
to asymptotic shells, in "Plates and Shells", M. Fortin, ed., pp. 125-158, CRM Proc. Lect.
Notes ser., Vol. 21, AMS Publications, Providence, R.I. 1999 (1996 CMS Annual Seminar,
Quebec City). (34 pages) (American Mathematical Society, Providence, R.I.)
- M.C. DELFOUR, Méthodes intrinsèques pour le contrôle et l'optimisation
des coques minces, in "Elasticité, Viscoélasticité et Contrôle
Optimal", J. Blum, A. Raoult, J. Baranger, eds, ESAIM Proceedings, Vol.2, 1997, pp. 65-86,
URL: http://www.emath.fr/proc/Vol.2/, (Huitièmes Entretiens du Centre Jacques Cartier,
Lyon, France, décembre 1995) (22 pages)
- M.C. DELFOUR and J.P. ZOLESIO, Hidden boundary smoothness for some classes of
differential equations on submanifolds, in "Optimization methods in partial differential
equations", S. Cox and I. Lasiecka, eds, pp. 59-73, Contemporary Mathematics, vol. 209, AMS
Publications, Providence, R.I., 1997, (1996 Joint Summer Research Conference on
Optimization Methods in PDE's, Mt Holyoke , USA) (15 pages) (American Mathematical Society,
Providence, R.I.)
- M.C. DELFOUR and J.P. ZOLESIO, Convergence to the asymptotic model for linear thin
shells, in "Optimization methods in partial differential equations", S. Cox and I.
Lasiecka, eds, pp. 75-93, Contemporary Mathematics, vol. 209, AMS Publications, Providence,
R.I., 1997 (1996 Joint Summer Research Conference on Optimization Methods in PDE's, Mt
Holyoke, USA) (18 pages) (American Mathematical Society, Providence, R.I.)
- M.C. DELFOUR and J.P. ZOLESIO, Curvatures and skeletons in shape optimization,
Zeitschrift für Angewandte Mathematik und Mechanik 76, Suppl. 3 (1996), 199-202 (ICIAM
1995, Hamburg, Germany, July 3-7, 1995).(4 pages).
- M.C. DELFOUR and J.P. ZOLESIO, New intrinsic models for shells, Zeitschrift für
Angewandte Mathematik und Mechanik 76, Suppl. 2 (1996), 77-80 (ICIAM 1995, Hamburg,
- M.C. DELFOUR et J. P. ZOLESIO, Differential equations for linear shells: comparison
between intrinsic and classical models, in ``Advances in the Mathematical Sciences-CRM's 25
years, (Luc Vinet,ed.), pp. 42-124, CRM Proc. Lecture Notes, vol. 11, Amer. Math. Soc.,
Providence, RI, 1998.(83 pages) (American Mathematical Society, Providence, R.I.)
- M.C. DELFOUR, Intrinsic modelling of shells, in "Modelling and Optimization of
Distributed Parameter Systems: Applications to engineering, K. Malanovski, Z. Nahorski and
M. Peszy´nska, eds, pp.16-30, Chapman & Hall, London, New York 1996 (IFIP
Conference on "Modelling and optimization of distributed parameter systems with
applications to engineering", Warsaw, Poland, July 17-21, 1995). 73K15 (49Q15)
- M.C. DELFOUR and J.P. ZOLESIO, Modelling and control of thin/shallow shells, in
"Control of Partial Differential Equations and Applications", E. Casas, ed., pp. 51-62,
Marcel Dekker, New York, Basel, Hong Kong 1996 (IFIP Conference on Control of PDE and
Applications, Laredo, Spain, Sept. 5-9, 1994) (12 pages)
- M.C. DELFOUR and J.P. ZOLESIO, Distance functions, curvatures and shell theory, in
"Curvature flows and related topics", A. Damlamian, J. Spruck and A. Visintin, eds, pp.
47-66, Mathematical Sciences and Applications, GAKUTO Internat. Ser. Math. Sci. Appl., 5,
Gakkotosho, Tokyo 1995 (Second Int. Con. on Motion by mean curvature and related topics,
Levico (Trento), Italy, June 27-July 2 1994) (20 pages) 73K15 (49Q20 73V25)
- M.C. DELFOUR and J.P. ZOLESIO, The optimal design problem of Céa and Malanowski
revisited, in "Optimal Design and Control", J. Borggaard, J. Burkardt, M. Gunzburger, and
J. Peterson, eds, pp. 133-150, Birkhäuser Boston, Inc., Boston, Basel, Berlin 1995 (18
pages) (Workshop on Optimal Design and Control, Blacksburg, Va., April 8-9, 1994)
- M.C. DELFOUR, Z. MGHAZLI and J.P. ZOLESIO, Computation of shape gradients for mixed
finite element formulations, in "Partial Differential Equations Methods in Control and
Shape Analysis", G. Da Prato and J.P. Zolésio, eds, pp. 77-93, Marcel Dekker, New York
1997 (IFIP Conference on PDE Methods in Control and Shape Analysis, Trento, Italie
décembre 1994) (17 pages)
- M.C. DELFOUR and J.P. ZOLESIO, On a geometrical bang-bang principle for some compliance
problems, in "Partial Differential Equations Methods in Control and Shape Analysis", G. Da
Prato and J.P. Zolésio, eds, pp. 95-109, Marcel Dekker, New York 1997 (IFIP Conference
on PDE Methods in Control and Shape Analysis, Trento, Italie décembre 1994) (15
pages)
- M.C. DELFOUR and J.P. ZOLESIO, On a variational equation for thin shells, in "Control
and Optimal Design of Distributed Parameter Systems", J. Lagnese, D. Russell, L. White,
eds, pp. 25-37, IMA Series, Springer-Verlag, New York 1994 (IMA, Minneapolis, November
9--13, 1992) (13 pages)
- M.C. DELFOUR and J.P. ZOLESIO, Oriented distance functions in shape analysis and
optimization, in "Control and Optimal Design of Distributed Parameter Systems", J.Lagnese,
D. Russell, L. White, eds, pp. 39-72, IMA Series, Springer-Verlag, New York 1994 (IMA
workshop on "Control and Optimal Design of Distributed Parameter Systems, November 9-13,
1992, IMA, Minn.) (34 pages)
- M.C. DELFOUR et J. MORGAN, Derivative of saddle points under relaxed assumptions, dans
"Proc. IEEE Conference on Decision and Control", pp. ??-??, IEEE Publications, New York
1992. (31st IEEE Conference on Decision and Control, December 16-18, 1992, Tuckson,
Arizona) (2 pages) (Institute of Electrical and Electronics Engineers, New York)
- M.C. DELFOUR and J.P. ZOLESIO, Functional analytic methods in shape analysis, in
"Boundary Control and Variation", J.-P. Zolésio, ed., Chapter 6, pp. 105-139, Marcel
Dekker, New-York 1994. (Proc. Workshop on Boundary Control and Boundary Variations,
Sophia-Antipolis, France, June 3-5, 1992) (35 pages)
- M.C. DELFOUR and S. TOWAIJ, Spectrum Quality Indicators for the land mobile system, in
"Proc. IEEE 41st Vehicular Technology Society", pp. 710-715, IEEE Publishing Services, New
York 1991 (1991 IEEE 41st Vehicular Technology Society, St. Louis Miss., May 20-22, 1991)
(6 pages) (Institute of Electrical and Electronics Engineers, New York)
- M.C. DELFOUR and J. MORGAN, Differentiability of MinMax and saddle points with relaxed
assumptions, in "Boundary Control and Boundary Variations", J.-P. Zolésio, ed., pp.
174-185, LNCIS Vol. 178, Springer-Verlag, New-York, Berlin, Heidelberg 1992. (Proc.
Workshop on Boundary Control and Boundary Variations, Sophia-Antipolis, France, October
15-17, 1990) (11 pages)
- M.C. DELFOUR and A. OUANSAFI, New Noniterative approximations to the solution of the
old matrix Riccati differential equation, in "Boundary Control and Boundary Variations",
J.-P. Zolésio, ed., pp. 186-201, LNCIS Vol. 178, Springer-Verlag, New-York, Berlin,
Heidelberg 1992. (Proc. Workshop on Boundary Control and Boundary Variations,
Sophia-Antipolis, France, October 15-17, 1990) (16 pages)
- A. CHALIFOUR and M.C. DELFOUR, Optimal Control in World Health Problems: Onchocerciasis
Control, in "Proc. 29th IEEE Conference on Decision and Control", pp. 2949-2954, IEEE
Publications, New York 1990 (29th IEEE Conference on Decision and Control, Honolulu,
Hawaï, December 5-7, 1990), (6 pages) (Institute of Electrical and Electronics
Engineers, New York)
- M.C. DELFOUR and J.P. ZOLESIO, Adjoint state for control of variational inequalities,
in "Emerging applications in free boundary problems", John M. Chadam and Henning Rasmussen,
eds, pp. 215-223), Pitman Research Notes in Mathematics Series, Vol. 280, Longman
Scientific & Technical, Harlow, Essex, UK 1993. (Fifth International Colloquium on
"Free Boundary Problems: Theory and Applications", Montréal, Canada, June 13-22, 1990)
(9 pages)
- M.C. DELFOUR and J.P. ZOLESIO, Shape derivatives for non-smooth domains, in "Optimal
Control of Partial Differential Equations", K.-H. Hoffmann and W. Krabs, eds, pp. 38-55,
Springer-Verlag, Berlin, Heidelberg, New York 1991. (International Conference on Optimal
Control of Partial Differential Equations, Irsee, F.R. of Germany, April 9-12, 1990)
- M.C. DELFOUR and J.P. ZOLESIO, Shape Hessian by the Velocity Method: a Lagrangian
Approach, in "Stabilization of Flexible Structures", J.P. Zolésio, ed., pp.
255-279,Springer-Verlag, Berlin, Heidelberg, New-York, 1990. (CONCOM Workshop on
Stabilization of Flexible Structures, Montpellier, France, January 1989). (25 pages)
- G. Da PRATO and M.C. DELFOUR, Linear Quadratic Control Problem without Stability, in
"Stabilization of Flexible Structures", J.P. Zolésio, ed., pp. 126-147,
Springer-Verlag, Berlin, Heidelberg, New-York, 1990. (CONCOM Workshop on Stabilization of
Flexible Structures, Montpellier, France, January 1989). (23 pages)
Livres
- M.C. DELFOUR et J.-P. ZOLESIO, Intrinsic differential geometry and theory of thin
shells, Quaderni, Scuola Normale Superiore, (Pise, Italie), 2000 (213 pages) à
paraître.
- M.C. DELFOUR et J.-P. ZOLESIO, Shapes and geometries : analysis, differential calculus
and optimization, soumis pour publication, janvier 2000. (461 pages)
- M.C. DELFOUR, Boundaries, interfaces and transitions, CRM Proc. Lecture Notes Vol. 13,
Amer. Math. Soc., Providence, RI 1998 (Ecole d'été du CRM, Banff 1995). (343
pages)
- A. BENSOUSSAN, G. DA PRATO, M.C. DELFOUR et S.K. MITTER, Representation and Control of
Infinite Dimensional Systems, Volume II, Birkhäuser Boston, Inc., Boston, Basel,
Berlin, 1993. (345 pages)
- A. BENSOUSSAN, G. DA PRATO, M.C. DELFOUR et S.K. MITTER, Representation and Control of
Infinite Dimensional Systems, Volume I, Birkhäuser Boston, Inc., Boston, Basel, Berlin
1992. (315 pages)
- M.C. DELFOUR, Shape Optimization and Free Boundaries, Series C: Mathematical and
Physical Sciences, Kluwer Academic Publishers, Dordrecht, Boston, London 1992.
(Séminaire de Mathématiques Supérieures 1990, NATO-ASI Series). (462
pages)
Chapitre de livres
- M.C. DELFOUR and M.P. POLIS, On issues related to stabilization of large flexible space
structures, in "Control and Estimation in Distributed Parameter Systems", H.T. Banks, ed.,
pp. 41-84, SIAM Frontiers in Applied Mathematics series, Philadelphia, 1992 (44 pages)
(Society for Industrial and Applied Mathematics, Philadelphis, Penn.).
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