# Delfour, Michel

Ph.D. Case Western Reserve University 1970

## Contact :

• Téléphone 514-343-7265
Département de mathématiques et de statistique

## Research interests

Michel Delfour is a Guggenheim, Killam, and SIAM Fellow and was awarded the Urgel-Archambault Prize for Physics, Mathematics, and Engineering from ACFAS. His research interests are: optimization and design of shapes and geometries, analysis and control of ordinary, delay, and partial differential systems, control and stabilization of large space structures, numerical methods in differential equations and optimization. His recent interests include the frequency assignment methods to land mobiles, the modelling and control of thin and asymptotic shells, the design of endoprotheses in interventional cardiology, and the design of the dynamics of drug release. He is the author of 13 books and more than 175 papers.

He has been president of the Canadian Mathematical Society and has served on numerous Canadian granting and advisory committees, as well as on panels,  boards, and executive committees of international organizations. He has been a professional engineer (Ordre des Ingénieurs du Québec) since 1966 and has been involved in numerous consulting activities for Canadian organizations.

## Selected articles

• - , Three-dimensional quadratic model of paclitaxel release from biodegradable polymer films, accepté le 24 juin 2014, 1-19 () SIAM J. Appl. Math.
• - , Anisotropic mesh adaptation on Lagrangian Coherent Structures, 231,, 6419-6437 () Journal of Computational Physics
• - , Drug release kinetics from biodegradable polymers via partial differential equation models, 118, issue 1, , 161-183 () Acta Applicandae Mathematicae
• - , Quadratic models to fit experimental data of Paclitaxel release kinetics from biodegradable polymers, 71, No. 6, , 2269-2286 () SIAM J. Appl. Math. (Special Issue on Mathematical Modeling of Controlled Drug Delivery)
• - , New equations for the dose under pulsative/periodic conditions in the design of coated stents, 13, No. 1, , 19-34 () Computer Methods in Biomechanics and Biomedical Engineering
• - , Linear-quadratic differential games: closed loop saddle points, 47, No. 6, , 3138-3166 () SIAM J. on Control and Optim.
• - , Jean-Paul Zolésio---a short biography, 37, 743--745 () Control and Cybernetics
• - , Coupling Stokes and Darcy equations, 58, , 525-538 () Applied Numerical Mathematics
• - , General Patterns and Asymptotic Dose in the Design of Coated Stents, 11, issue 4, , 323-334 () Computer Methods in Biomechanics and Biomedical Engineering
• - , Representation of hypersurfaces and minimal smoothness of the midsurface in the theory of shells , 37, No. 4, , 879-911 () Control and Cybernetics
• - , Linear-Quadratic Differential Games: from finite to infinite dimension, 35, No. 4, , 431-446 () Applicationes Mathematicae
• - , Uniform Fat Segment and Cusp Properties for Compactness in Shape Optimization, 46, No. 2, , 385-419 () Appl Math Optim
• - , Linear-Quadratic Differential Games: Saddle Point and Riccati Differential Equation, 46, No. 2, , 750-774 () SIAM J. Control and Optim.
• - , Evolution equations for shapes and geometries, 6, 399--417 () J. Evol. Equ.
• - , A numerical study of primal mixed finite element approximations of Darcy equations, 22, 901--915 () Comm. Numer. Methods Engrg.
• - , Shape identification via metrics constructed from the oriented distance function, 34, 137--164 () Control Cybernet.
• - , Modeling and design of coated stents to optimize the effect of the dose, 65, 858--881 (electronic) () SIAM J. Appl. Math.
• - , The new family of cracked sets and the image segmentation problem revisited, 4, 29--52 () Commun. Inf. Syst.
• - , Oriented distance function and its evolution equation for initial sets with thin boundary, 42, 2286--2304 (electronic) () SIAM J. Control Optim.
• - , Dynamical free boundary problem for an incompressible potential fluid flow in a time-varying domain, 12, 1--25 () J. Inverse Ill-Posed Probl.
• - , Characterization of the space of solutions of the membrane shell equation for arbitrary $C^{1,1}$ midsurfaces, 28, 481--501 () Control Cybernet.
• - , Fixed mesh approximation of ordinary differential equations with impulses, 78, 377--401 () Numer. Math.
• - , Error analysis of mixed finite elements for cylindrical shells, 7, 261--277 () Adv. Comput. Math.
• - , On the design and control of systems governed by differential equations on submanifolds, 25, 497--514 () Control Cybernet.
• - , Tangential differential equations for dynamical thin/shallow shells, 128, 125--167 () J. Differential Equations
• - , A boundary differential equation for thin shells, 119, 426--449 () J. Differential Equations
• - , One-sided derivative of minmax and saddle points with respect to a parameter, 31, 343--358 () Optimization
• - , Shape analysis via oriented distance functions, 123, 129--201 () J. Funct. Anal.
• - , Noniterative approximations to the solution of the matrix Riccati differential equation, 29, 1648--1693 () SIAM J. Numer. Anal.
• - , A complement to the differentiability of saddle points and min-max, 13, 87--94 () Optimal Control Appl. Methods
• - , Optimal distribution of larvicide in running waters, 2, 264--303 () SIAM J. Optim.
• - , Structure of shape derivatives for nonsmooth domains, 104, 1--33 () J. Funct. Anal.
• - , Unbounded solutions to the linear quadratic control problem, 30, 31--48 () SIAM J. Control Optim.
• - , Anatomy of the shape Hessian, 159, 315--339 () Ann. Mat. Pura Appl. (4)
• - , Velocity method and Lagrangian formulation for the computation of the shape Hessian, 29, 1414--1442 () SIAM J. Control Optim.
• - , Analyse des problèmes de forme par la dérivation des minimax, 6, 211--227 () Ann. Inst. H. Poincaré Anal. Non Linéaire
• - , Shape sensitivity analysis via a penalization method, 151, 179--212 () Ann. Mat. Pura Appl. (4)
• - , Shape sensitivity analysis via min max differentiability, 26, 834--862 () SIAM J. Control Optim.
• - , Approximation of nonlinear problems associated with radiating bodies in space, 24, 1077--1094 () SIAM J. Numer. Anal.
• - , State space theory of linear time invariant systems with delays in state, control, and observation variables. I, II, 125, 361--450 () J. Math. Anal. Appl.
• - , Modeling, stabilization and control of serially connected beams, 25, 526--546 () SIAM J. Control Optim.
• - , Stabilization of hyperbolic systems using concentrated sensors and actuators, 31, 1091--1096 () IEEE Trans. Automat. Control
• - , The linear-quadratic optimal control problem with delays in state and control variables: a state space approach, 24, 835--883 () SIAM J. Control Optim.
• - , Dérivation d'un min max et application à la dérivation par rapport au contrôle d'une observation non différentiable de l'état, 302, 571--574 () C. R. Acad. Sci. Paris Sér. I Math.
• - , Discontinuous polynomial approximations in the theory of one-step, hybrid and multistep methods for nonlinear ordinary differential equations, 47, 169--189, S1--S8 () Math. Comp.
• - , An optimal triangulation for second-order elliptic problems, 50, 231--261 () Comput. Methods Appl. Mech. Engrg.
• - , Linear optimal control of systems with state and control variable delays, 20, 69--77 () Automatica J. IFAC
• - , Optimal design of minimum weight thermal diffuser with constraint on the output thermal power flux, 9, 225--262 () Appl. Math. Optim.
• - , Finite-difference solutions of a nonlinear Schrödinger equation, 44, 277--288 () J. Comput. Phys.
• - , Discontinuous Galerkin methods for ordinary differential equations, 36, 455--473 () Math. Comp.
• - , The structural operator $F$ and its role in the theory of retarded systems. II, 74, 359--381 () J. Math. Anal. Appl.
• - , The structural operator $F$ and its role in the theory of retarded systems. I, 73, 466--490 () J. Math. Anal. Appl.
• - , The largest class of hereditary systems defining a $C_{0}$ semigroup on the product space, 32, 969--978 () Canad. J. Math.
• - , $F$-reduction of the operator Riccati equation for hereditary differential systems, 14, 385--395 () Automatica---J. IFAC
• - , State theory of linear hereditary differential systems, 60, 8--35 () J. Math. Anal. Appl.
• - , The linear quadratic optimal control problem for hereditary differential systems: theory and numerical solution, 3, 101--162 () Appl. Math. Optim.
• - , Stability and the infinite-time quadratic cost problem for linear hereditary differential systems, 13, 48--88 () SIAM J. Control
• - , Hereditary differential systems with constant delays. II. A class of affine systems and the adjoint problem, 18, 18--28 () J. Differential Equations
• - , Individual and collective rationality in a dynamic Pareto equilibrium, 13, 290--302 () J. Optimization Theory Appl.
• - , Function spaces with a projective limit structure, 42, 554--568 () J. Math. Anal. Appl.
• - , Hereditary differential systems with constant delays. I. General case, 12, 213--235; erratum, ibid. 14\ (1973), 397 () J. Differential Equations
• - , Controllability and observability for infinite-dimensional systems, 10, 329--333 () SIAM J. Control
• - , Controllability, observability and optimal feedback control of affine hereditary differential systems, 10, 298--328 () SIAM J. Control
• - , Le contrôle optimal de systèmes gouvernés par des équations différentielles héréditaires affines, 272, A1715--A1718 () C. R. Acad. Sci. Paris Sér. A-B
• - , Systèmes d'équations différentielles héréditaires à retards fixes. Une classe de systèmes affines et le problème du système adjoint, 272, A1109--A1112 () C. R. Acad. Sci. Paris Sér. A-B
• - , Systémes d'équations différentielles héréditaires à retards fixes. Théorèmes d'existence et d'unicité, 272, A382--A385 () C. R. Acad. Sci. Paris Sér. A-B
• - , Reachability of perturbed systems and ${\rm min\,sup}$ problems, 7, 521--533 () SIAM J. Control

## Peer-reviewed papers

• - , Metrics spaces of shapes and geometries from set parametrized functions, dans "New trends in Shape Optimization," A. Pratelli and G. Leugering, eds, 57-101 () International Series of Numerical Mathematics, Birkhäuser Verlag.
• - , Quadratic ODE and PDE models of drug release kinetics from biodegradable polymers, dans "25th IFIP TC7 Conference on System Modeling and Optimization", Dietmar Hömberg et Fredi Tröltzsch, eds, 13-24 () IFIP Adv. Inf. Commun. Technol., Springer, Berlin.
• - , Boundary smoothness of the solution of Maxwell's equations of electromagnetics, dans "System modeling and optimization", 492-506 () IFIP Adv. Inf. Commun. Technol., 312, Springer, Berlin.
• - , Representations, composition, and decomposition of C1,1 hypersurfaces, dans "Optimal control of coupled systems of partial differential equations", 85-104 () Internat. Ser. Numer. Math., 158, Birkhäuser Verlag, Basel.
• - , Shape and geometric methods in image processing, dans "Free and moving boundaries analysis, simulation, and control", 293-308 () Lecture Notes in Pure and Applied Mathematics Volume 252, Chapman & Hall/CRC, Boca Raton, FL.
• - , Some New Results in Open and Closed-Loop Linear-Quadratic Differential Games, dans "Proceedings 16th IEEE Mediterranean Conference on Control and Automation", 907-912 () IEEE Publications.
• - , The uniform fat segment and cusp properties in shape optimization, dans "Control and Boundary Analysis", J. Cagnol and J.-P. Zolésio, eds, 85-96 () Lect. Notes in Pure and Appl. Math. Vol. 240, Chapman & Hall/CRC, Boca Raton, FL.
• - , Uniform cusp property, boundary integral, and compactness for shape optimization, dans "System Modeling and Optimization", J. Cagnol and J.-P. Zolésio, eds, 25-40 () IFIP Int. Fed. Inf. Process., 166, Kluwer Acad. Publ., Boston, MA.
• - , Extension of the uniform cusp property in shape optimization, in "Control Theory of Partial Differential Equations", O. Emanuvilov, G. Leugering, R. Triggiani, and B. Zhang, eds, 71-86 () IFIP Int. Fed. Inf. Process., 166, Kluwer Acad. Publ., Boston, MA.

## Monographs and proceedings

• - , Arterial Stenosis: Hemodynamics and Drug Elutions, dans « PanVascular Medicine », 2nd ed., Peter Lanzer, ed., Volume 1, Part IV, Chapter 24, 781-868 () Springer Heidelberg New York Dordrecht London.
• - , Introduction to optimization and semi-differential calculus () série SIAM-MOS, Society for Industrial and Applied Mathematics, Philadelphia, USA. ISBN 978-1-611972-14-6.
• - , Introduction à l'optimisation et au calcul semi-différentiel () Collection: Sciences Sup., Mathématiques appliqués pour le Master/SMAI, Dunod, Paris. ISBN 978-2-10-057423-0.
• - , Shapes and Geometries: Metrics, Analysis, Differential Calculus and Optimization () SIAM series on Advances in Design and Control, Society for Industrial and Applied Mathematics, Philadelphia, USA. ISBN 978-0-898719-36-9.
• - , Representation and Control of Infinite Dimensional Systems () Birkhäuser Boston, Inc., Boston, Basel, Berlin.
• - , High Dimensional Partial Differential Equations in Science and Engineering () CRM Lecture Notes and Proceedings, vol 41, AMS Publ, R.I., ISBN-13 978-0-8218-3853-2.
• - , Quantum Control: Mathematical and Numerical Challenges () CRM Lecture Notes and Proceedings, vol 33, AMS Publ, R.I., ISBN 0-8218-3330-8.
• - , Shapes and Geometries: Analysis, Differential Calculus and Optimization () SIAM series on Advances in Design and Control, Society for Industrial and Applied Mathematics, Philadelphia, USA. ISBN 0-89871-489-3.
• - , Boundaries, interfaces and transitions () CRM Proc. Lecture Notes Vol. 13, Amer. Math. Soc., Providence, RI. ISBN 0-8218-0505-3.
• - , Representation and Control of Infinite Dimensional Systems, II () Birkhäuser Boston, Inc., Boston, Basel, Berlin, ISBN 0-8176-3642-0, ISBN 3-7643-3642-0.
• - , Shape Optimization and Free Boundaries () Series C: Mathematical and Physical Sciences, Vol 380, Kluwer Academic Publishers, Dordrecht, Boston, London. ISBN 0-7923-1944-3.
• - , Representation and Control of Infinite Dimensional Systems, I () Birkhäuser Boston, Inc., Boston, Basel, Berlin. ISBN 0-8176-3641-2, ISBN 3-7643-3641-2.
• - , Compte rendu du Deuxième Colloque CRM-IRIA, 1, no. 2 () Ann. Sci. Math. Québec
• - , Actes du Colloque sur la théorie des systèmes et la gestion scientifique des services publics () ACFAS - CRM - HEC, Montréal.