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Aziz Belmiloudi, PhD hab. Senior
Associate Professor (Aziz.
Belmiloudi at math.cnrs.fr) IRMAR (Institut
de Recherche Mathématique de Rennes)
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Topics : PDEs/ODEs, Control theory, Coupled Systems, Hybrid Systems, Time-delay Systems, Applied analysis and Mathematical modelling As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality.» Albert Einstein |
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Scientific Publications : Books:
Edited Books:
Invited Book Chapters: 73. A. Belmiloudi, Coupled PDEs and Control systems arising in Climate
Dynamics: Ocean-Atmosphere Interactions and Tropical Instability Waves. In
Edited Book:Mathematical Research Summaries (Matthew A. Rowe ed.), Vol. 1, Chapter 105, Nova
Science Publishers, New York, 2017. 72. S. Corre, A. Belmiloudi. Coupled Lattice Boltzmann Modeling of Bidomain type models in Cardiac Electrophisiology.
Mathematical and Computational Approaches in Advancing Modern Science and Engineering
(eds. J. Bélair,
I. Frigaard,
H. Kunze,
R., Melnik,
J. Spiteri), Springer cham, Switzerland, 2016. Book link 71. A. Belmiloudi. Coupled PDEs and Control systems arising in Climate Dynamics:
Ocean-Atmosphere Interactions and Tropical Instability Waves. In Edited Book: Partial Differential Equations: Classification,
Properties and Applications (D.E. Richards ed.), Chapter 2, Nova Science Publishers, New York, 15-71, 2015.
Book link 70. A. Belmiloudi. Nonlinear robust control and regulation problems for biomedical
dynamical systems. In. Interdisciplinary Topics in Applied Mathematics, Modeling, and Computational Science (eds. M. Cojocaru, I.S. Kotsireas,
R. Makarov,
R. Melnik, H. Shodiev),
Vol. 117, Chapter 8, Serie Springer Proceedings in Mathematics and Statistics,
Springer Berlin Heidelberg, 49-56, 2015. Book link 69. A. Belmiloudi. Stabilization, Regulation and Robust Control of Uncertain processes
and parameters in Porous Medium systems with Applications. In Edited Book: Focus
on Porous Media Research (C. Zhao ed.), Chapter 6, Nova Science Publishers, New York, 165-228, 2013. Book link 68. A. Belmiloudi. Thermal Therapy: Stabilization and Identification. In Edited Book: Heat
Transfer-Mathematical Modelling, Numerical Methods and Information Technology (A. Belmiloudi ed.), Chapter 2, INTECH, Vienna, 33-76, 2011. http://dx.doi.org/10.5772/14450 International Refereed Journals Articles: 67. A. Belmiloudi, Brain Connectivity Dynamics
and Mittag–Leffler
Synchronization in Asymmetric Complex Networks for a Class of Coupled
Nonlinear Fractional-Order Memristive Neural
Network System with Coupling Boundary Conditions, Axioms, vol. 13, No.7, [47 pages], 2024. (Highlighted by Life Science Weekly, 13 Aug,
2024, p.4570, NewsRx, Atlanta, GA). 66. A. Belmiloudi, On Behavior of
Solutions for Nonlinear Klein–Gordon Wave Type Models with a Logarithmic
Nonlinearity and Multiple Time-Varying Delays, Axioms,
vol. 13, No.1, [20 pages], 2024. 65. A. Belmiloudi, Cardiac memory phenomenon, time-fractional order nonlinear system and bidomain-torso type model in electrocardiology, AIMS Mathematics, vol. 6, No.1, 821-867, 2021. (Highlighted by Obesity, Fitness & Wellness Week,
23 Jan. 2021, p.3679, NewsRx, Atlanta, GA). 64. S. Corre, A. Belmiloudi, Coupled
lattice Boltzmann simulation method for bidomain
type models in cardiac electrophysiology with multiple time-delays, Mathematical
Modelling of Natural Phenomena, vol. 14, No. 2, pp. 27., 2019. 63. A. Belmiloudi, Time-varying delays in electrophysiological wave propagation along
cardiac tissue and minimax control problems associated with uncertain bidomain type models, AIMS Mathematics, vol. 4, No. 3, 928-983, 2019.
(Highlighted by Contemporary Women's Issues, Cardiovascular Week, 5 Oct. 2019, p.885, NewsRx, Atlanta, GA). 62. A. Belmiloudi, S.
Corre , Mathematical modeling and analysis of
dynamic effects of multiple time-varying delays on electrophysiological wave
propagation in the heart, Nonlinear Analysis
Series B: Real World Applications, vol. 47, 18-44, 2019. (Highlighted by Mathematics Week, 4 june,
2019, p.679, NewsRx, VerticalNews, Atlanta, GA). 61. A. Belmiloudi. Optimal control for
chemotaxis systems and adjoint-based optimization
with multiple-relaxation-time lattice Boltzmann models, Journal of
Mathematics and Biostatistics, vol. 1, No. 1, 32-67, 2018 (by invitation for the launch of the journal) 60. A. Belmiloudi. Mathematical modeling and optimal control problems in brain tumor targeted drug delivery strategies, International
Journal of Biomathematics, vol. 10, 1750056, [62 pages], 2017. 59. S. Corre, A. Belmiloudi. Coupled
lattice Boltzmann method for numerical simulations of fully coupled heart and
torso bidomain system in electrocardiology,
Journal of Coupled Systems and Multiscale Dynamics, vol. 4, No. 3, 207-229, 2016. 58. M. Penet, H. Guéguen, A.
Belmiloudi. Saddle
Point MPC Approach to Nonlinear Robust Sampled Data Control problem, International Journal of Control, Automation and Systems, vol. 14,
issue 1, 222-233, 2016. 57. A. Belmiloudi. Dynamical
behavior of nonlinear impulsive abstract partial
differential equations on networks with multiple time-varying delays and
mixed boundary conditions involving time-varying delays, Journal of
Dynamical and Control Systems, vol.
21, No 1, 95-146, 2015. 56. A. Belmiloudi, F.
Mahé. On nonlinear inverse
problems of heat transfer with radiation boundary conditions. Application to dehydratation of gypsum plasterboards exposed to fire,
Advance in Numerical Analysis, vol. 2014,
Article ID 634712,
18 pages, 2014. 55. A. Belmiloudi. Robust
control problem of uncertain bidomain models in
cardiac electrophysiology, Journal of Coupled Systems and Multiscale
Dynamics, vol. 1, No. 3, 332-350, 2013. 54. A. Rasheed, A.
Belmiloudi. Mathematical
modelling and numerical simulation of dendrite growth using phase-field
method with a magnetic field effect, Communications in Computational
Physics, vol. 14, No. 2, 477-508, 2013. 53. A. Rasheed, A.
Belmiloudi. An
analysis of a phase-field model for isothermal binary alloy solidification
with convection under the influence of magnetic field, Journal of Mathematical
Analysis and Applications, vol. 390, 244-273, 2012. 52. A. Rasheed, A.
Belmiloudi, F. Mahé. Dynamics
of dendrite growth in a binary alloy with magnetic field effect, Discrete
and Continuous Dynamical Systems, vol. 2011, special issue, 1224-1233,
2011. 51. A. Belmiloudi. Parameter identication problems and analysis
of the impact of porous media in biofluid heat
transfer in biological tissues during thermal therapy, Nonlinear
Analysis Series B: Real World Applications, vol. 11, No.3, 1345-1363, 2010. (Highlighted by Health and
Medicine Week, July 26, 2010, p.2636, ISSN: 15316459). 50. A. Belmiloudi. Analysis
of the impact of nonlinear heat transfer laws on temperature distribution in
irradiated biological tissues: mathematical models and optimal controls, Journal
of Dynamical and Control Systems, vol. 13, No. 2, 217-254, 2007. 49. A. Belmiloudi. Bilinear minimax control problems for a class of parabolic systems
with applications to control of nuclear reactors, Journal of Mathematical Analysis and Applications, vol. 327, No. 1, 620-642, 2007. 48. A. Belmiloudi. Robust
control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems, Abstract and
Applied Analysis,
vol. 2006, Article ID 26724, 43 pages, 2006. 47. A. Belmiloudi. On some control problems for heat transfer systems in perfused
biological tissues, WSEAS Transactions on Systems, vol.5, No.1,
17-25, 2006. 46. A. Belmiloudi. Minimax control problem of periodic competing parabolic systems with logistic
growth terms, International Journal of
Control, vol.79, No.2, 150-161, 2006. 45. A. Belmiloudi, J.P. Yvon. Robust control of a non-isothermal solidification model, WSEAS
Transactions on Systems, vol.4, No.12, 2291-2300, 2005. 44. A. Belmiloudi. Nonlinear
optimal control problems of degenerate parabolic equations with logistic
time-varying delays of convolution type, Nonlinear Analysis Series A:
Theory, Methods & Applications, vol. 63,
1126-1152, 2005. 43. A. Belmiloudi, G. Le Meur.
Mathematical
and numerical analysis of dehydratation of gypsum
plasterboards exposed to fire, Applied Mathematics and Computation, vol.163, No.3, 1023-1042, 2005. 42. A. Belmiloudi. Optimal control problems of nonlinear degenerate parabolic
differential systems with logistic time-varying delays, IMA Journal of Mathematical Control and Information, vol.22, No.1, 88-108, 2005. 41. A. Belmiloudi. Robust and optimal control problems to a phase-field model for the
solidification of a binary alloy with a constant temperature, Journal of
Dynamical and Control Systems, vol.10, No.2,453-499, 2004. 40. A. Belmiloudi. On some robust control problems for nonlinear parabolic equations, International
Journal of Pure and Applied Mathematics, vol.11, No.2, 119-151, 2004. 39. A. Belmiloudi. Robust control problems associated with time-varying delays nonlinear
parabolic equations, IMA Journal of Mathematical Control and Information, vol.20, No.3, 305-334, 2003. 38. A. Belmiloudi. Nonlinear robust control problems of parabolic type equations with
time-varying delays given in the integral form, Journal of
Dynamical and Control Systems, vol.9,
No.4, 469-512, 2003. 37. A. Belmiloudi. Mathematical analysis and optimal control problems for the perturbation
of the primitive equations of the ocean with vertical viscosity, Journal
of Applied Analysis, vol.8, No.2, 153-200, 2002. 36. A. Belmiloudi. Robin-type boundary control problems for the nonlinear Boussinesq type equations, Journal of Mathematical
Analysis and Applications, vol.273, No.2, 428-456, 2002. 35. A. Belmiloudi. Existence and characterization of an optimal control for the problem
of long waves in a Shallow-Water model, SIAM Journal on Control and
Optimization, vol.39, No.5, 1558-1584, 2001. 34. A. Belmiloudi. Asymptotic behaviour of the perturbation of the primitive equations
of the ocean with vertical viscosity, Canadian Applied Mathematics
Quarterly, vol.8, No.2, 97-140, 2000. 33. A. Belmiloudi. Regularity results and optimal control problems for the perturbation
of Boussinesq equations of the ocean, Numerical
Functional Analysis and Optimization, vol.21, No
5&6, 623-651, 2000. 32. A. Belmiloudi, F. Brossier, L. Monier. Mathematical and numerical modelization of
large-scale oceanic waves, Mathematical Methods in the Applied Sciences, vol.22, 967-999, 1999. 31. A. Belmiloudi. A nonlinear optimal control problem for assimilation of surface data
in a Navier-Stokes type equations related to
oceanography, Numerical Functional Analysis and Optimization, vol.20,
No 1&2, 1-26, 1999. 30. A. Belmiloudi, F.
Brossier. Regularity
results for a Navier-Stokes type problem related to
oceanography, Acta Applicandae Mathematicae, vol.48,
No.3, 299-316, 1997. 29. A. Belmiloudi, F.
Brossier. A control method for assimilation of surface data in a linearized Navier-Stokes type problem related to oceanography, SIAM
Journal on Control
and Optimization, vol.35, No.6, 2183-2197, 1997. International Conference Proceedings (with Referee) : 28. M. Penet, H. Guéguen, A.
Belmiloudi. Artificial Blood Glucose Control Using a DDE Modelling Approach, In. Proceeding
of 19th IFAC World Congress, pp. 2076– 2081, Vol. 19, Capetown, 2014 (ISBN:
978-3-902823-62-5). 27. M. Penel, H. Guéguen and A.
Belmiloudi. A
Robust Receding Horizon Control Approach to Artificial Glucose Control for
Type 1 Diabetes In. 9th IFAC Symposium on Nonlinear Control Systems,
IFAC-papersOnline, (eds. S. Tarbouriech,
M.Krstic), pp. 833-838, 2013 (ISBN:
978-3-902823-47-2). 26. R. Bourdais, H. Guéguen and A.
Belmiloudi. Distributed model predictive
control for a class of hybrid system based on Lagrangian
relaxation, In. Analysis and Design of Hybrid Systems, IFAC-papersOnline, (eds. M. Heemels, B. De Schutter, M. Lazar), pp. 46-51, 2012 (ISBN
978-3-902823-00-7). 25. M. Penet, H. Guéguen et A. Belmiloudi. Regulation Artificielle de la Glycemie : Developpement d'une commande robuste, In. Proceedings of the 7th IEEE Conférence Internationale Francophone d'Automatique (CIFA), pp. 425-430, 2012. 24. A. Maalouf, C. Bastianelli,
F. Mahé, A. Belmiloudi, M. Gadonna and D. Bosc. Improved integrated resonators in polymer technology for tunable filter, In. Silicon Photonics and Photonic
Integrated Circuits III, Vol. 8431, SPIE Proceedings, (eds., L. Vivien,
S.K. Honkanen, L. Pavesi,
S. Pelli), (ISBN 9780819491237), pp.
843124/1-843124/15, 2012 (supported by ANR, Images&Reseaux
cluster and Brittany Region). 23. A. Belmiloudi. Regulation of uncertain nonlinear systems: a differential equation
approach to robust control design with applications to biological systems, International
Congress of Mathematicians, Hyderabad, India, (eds., R.
Bhatia et al.), Hindustan Book Agency, pp. 466-467, 2010 (supported by
French National Committee of Mathematicians (CNFM)). 22. A. Rasheed, A.
Belmiloudi. Phase-field method for
computationally efficient modeling of the
solidification of binary alloy with magnetic field effect, In. Proceedings
of the NumAn2010 Conference in Numerical Analysis; Recent Approaches to
Numerical Analysis: Theory, Methods and Applications, (eds., V. Dougalis, E. Gallopoulos, A. Hadjidimos et al.), pp. 222-230, 2010 (ISBN
978-960-8475-14-4). 21. A. Belmiloudi, J.P. Yvon. Optimal control of a non-isothermal solidification model, In.
Proceedings of the WSEAS Inter. Conf. on Dynamical System and Control,
pp. 1-6, 2005 (ISBN:960-8457-37-8), Invited paper. 20. A. Belmiloudi. Optimal control related to effects of microwave heating on thermal
states of biological bodies, In. Proceedings of the WSEAS Inter. Conf. on
Dynamical System and Control, pp. 7-12, 2005 (ISBN:960-8457-37-8), Invited
paper. 19. A. Belmiloudi. Analysis of robust control problems for a quasilinear parabolic
equations, In. Proceedings of the 9th IEEE MMAR, "Optimisation of
Infinite Dimensional Systems" (eds., R. Kaszynski), Wydawnictwo Uczelniane Politechniki Szczecinskiej, pp.
99-108, 2003 (ISBN: 83-88764-82-9), Invited paper. 18. A. Belmiloudi. Mathematical and computional methods of an
optimal control for the primitive equations in a coupled atmosphere-ocean
model, In. Proceedings of the 9th IEEE MMAR, "Optimisation of
Infinite Dimensional Systems" (eds., R.
Kaszynski), Wydawnictwo Uczelniane
Politechniki Szczecinskiej,
pp. 87-96, 2003, (ISBN: 83-88764-82-9), Invited paper. 17. A. Belmiloudi. Studies in Robin-type boundary control problems for the primitive
equation of the ocean, In. Proceedings of the 8th IEEE MMAR,
"Optimisation of Infinite Dimensional Systems" (eds., S. Domek and R. Kaszynski), Wydawnictwo Uczelniane Politechniki Szczecinskiej, pp.
159-166, 2002 (ISBN: 83-88764-61-6), Invited paper. 16. A. Belmiloudi. On some control problems in a shallow-water model, In.
Proceedings of the 40th IEEE Conference on Decision and Control, Orlando,
Florida, IEEE Control Society, pp. 4956-4961, 2001 (ISBN:0-7803-7061-9), Paper
proposed by SIAM. 15. A. Belmiloudi. Studies in linear and nonlinear optimal control problems for viscous
flows equations, Application of mathematics in Engineering and Business Sozopol. In. Proceedings of the XXVI Summer School Sozopol (eds., B.I. Cheshankov and
M.D. Todorov), Heron Press, Sofia, 181-188, 2001
(ISBN: 954-580-094-1) . 14. A. Belmiloudi. Resolution of optimal control problem for a perturbation linearized Navier-Stokes type equations, Application of mathematics
in Engineering and Business Sozopol. In.
Proceedings of the XXII Summer School, Sofia University Press, pp. 39-51,
1996 (Invited paper). 13. A. Belmiloudi. Method of characteristics and error estimates of the perturbation of
given mean flow, Application of mathematics in Engineering and Business Sozopol. In. Proceedings of the XXII Summer School,
Sofia University Press, pp. 25-38, 1996 (Invited paper). Abstract of International Conferences (with Referee): 12. A. Belmiloudi, F.
Mahé, Optimal
control and parameter estimation in some epidemiological models, 21th
International Epidemiological Association (IEA) World Congress of Epidemology (WCE), August 19-22, Tokyo Area, Japan, 2017.
11. S. Corre, A. Belmiloudi. Mathematical modeling and lattice Bolzmann simulation method for bidomain
type models in cardiac electrophysiology with time-varying delays.
Conference on Complex Dynamical Systems in Life Sciences: Modeling
and Analysis, October 26-28, Agadir, Morocco, 2016. 10. A. Rasheed, A.
Belmiloudi. Optimal control of dendrite structure using magnetic field, in
Special Session : Nonlinear evolution PDEs,
interface and applications (Organizers. A. Miranville,
G. Caginalp and M. Grasselli),
AIMS Conferences on Dynamical Systems, Differential Equations and
Applications, July 1- 5, Orlando, Florida, USA, 2016. 9. M. Penet, H. Guéguen, A.
Belmiloudi, J.Y Poirier and I. Guilhem. A robust receding horizon approach for blood glucose control in type 1
diabetes, International Conference on Advanced Technologies and Treatments
for Diabetes (ATTD), Barcelona, Spain, 2012. 8. A. Belmiloudi, F. Mahé. Numerical resolution of long waves in a
Shallow-Water type model, International Symposium on Nonlinear Dynamics,
Shanghai, China, 2005. 7. A. Belmiloudi. Optimal control problems of nonlinear parabolic systems with logistic
time-varying delays, International Workshop on Shape optimization in life
sciences and environment, Toulouse, France, 2004. Other articles (Technical reports and non-peer reviewed publications): 6. A. Belmiloudi, J-L. Merrien.
New collocation methods for differential equations,
Laboratory LANS publication, 2000 (18 pp). 5. A. Belmiloudi, F. Brossier. Numerical
study of a control method computing an oceanic circulation from the observed
surface pressure, Laboratory IRMAR publication, rapport 00-53, 2000, (25 pp). 4. A. Belmiloudi. Discretization of the perturbation of a given mean flow: convergence, stability and error estimates. Laboratory LANS publication, vol.66, 1996, (37 pp). Habilitation to direct research : 3. Etudes théoriques et numériques de méthodes de contrôle optimal pour des équations primitives de l'océan et de l'atmosphère. Soutenue le 10 Juin 2002 (University de Rennes I). Jury : T. Colin (rapporteur), F.X. Le Dimet (rapporteur), E. Zuazua (rapporteur), G. Caloz, M. Crouzeix, M. Pierre, J.P. Yvon. PhD Thesis (Allocataire moniteur ): 2. Développement d'une méthode de contrôle optimal pour un problème de type Navier-Stokes: Application à la modélisation des courants océaniques par assimilation de mesures altimétriques. Soutenue le 20 Janvier 1995, Mention Très honorable). Jury : J. Blum (rapporteur), O. Pironneau (rapporteur), F. Brossier, G. Caloz, M. Crepon, M. Crouzeix, J. Rappaz. Master Thesis : 1. Discrétisation du problème PNS incompressible par une méthode d'éléments finis discontinus (P1-P2) [1]xQ1, 1991, Ecole Polytechnique Fédérale de Lausanne, EPFL (from Mathematics Institute of Computational Science and Engineering, Funded by Swiss metallurgical company Alusuisse-Lonza Group). Activities of general
interest:
Editorial Topic
Member of Axioms Editorial board
member of the following journals: - Research &
Reviews: Discrete Mathematical Structures - International
Journal of Advanced Mathematical Sciences - Journal of Advances in Shell Programming - Guest Editor of
Special Issue « Biomathematics »,
Applied Mathematics, 2013. N.B. I am also continuously reviewer of international research projects and
scientific journals Recent «ANR» Research Projects:
PhD students: - Amer Rasheed : "Dendritic Solidification of Binary Mixtures of Metals under the
action of Magnetic Field: Modeling, Mathematical
and Numerical Analysis", PhD Thesis Defended October 14th, 2010. Actually A. Rasheed is "Assistant Professor" at
LUMS Lahore University of Management Sciences, Department of Mathematics, Punjab, Pakistan. - Maxime Penet:
"Commande Prédictive nonlinéaire robuste par
méthode de point selle en optimisation sous contraintes. Analyse de stabilité
et application au diabète de type 1", PhD Thesis
Defended October 10th,
2013. Actually M. Penet is Senior Research Engineer (before that he was Assistant Professor at Supelec). - Samuel Corre: ''Méthodes de Boltzmann sur réseau pour la simulation numérique de certains systèmes d'advection-réaction-diffusion provenant de la physique et de la biologie, et analyse mathématique et numérique de problèmes issus du domaine biomédical cardio-vasculaire'', PhD Thesis Defended October 19th, 2018. N.B. I have also supervised and co-supervised some thirty of Master
students. Education: - Classes préparatoires aux grandes écoles (CPGE,) : MALHERBE High School in Caen; - Magistère of mathematics of Rennes and Master of mathematics and applications (Rennes1). |
