Publications

Key words

PDEs.
Multiscale phenomena.
Homogenization. Rigorous upscaling. Asymptotic analysis. Optimization.
Fluid mechanics.

Editorial activities

Editorial board, AIMS Journal of Dynamics and Games
J. Dyn. Games

Guest editor in chief, Special issue on optimization and differential equations, 2022
Discrete and Continuous Dynamical Systems-S

À venir
(coming soon...)

A multiscale lattice Boltzmann model for simulating Stokes to pre-Darcy flow
(with T. Coiffard)
Computer Methods in Applied Mechanics and Engineering (2026), doi

Improving learning for deep multi-sphere anomaly detection with conformal geometric algebra
(with J. de Saint Angel, C. Saint-Jean)
Recent Advances in Deep Learning Applications (2026)

Application of the polytopic approach for the Saint-Venant/shallow water equations
(with S. Bezzaoucha Rebai, A. El Ammari)
Computational Methods in Applied Sciences (2026)

Articles

Homogenized phase transition model for perforated ferromagnetic media
(with M. Ouhadan, M. Tilioua)
Proceedings of the Royal Society A (2025), doi

Homogenization tools for the routing management problem in dense network with transmission defects
(with M. Ouhadan, M. Tilioua)
Numer. Asymptotic Anal. (2025), doi

A network epidemic model: From the mathematical analysis to machine learning experiments
(with A. Mohamed Abdi)
Communications in Nonlinear Science and Numerical Simulation (2025), vol. 142, 108493, doi

New algorithm using an adaptive level set model applied to hippocampus segmentation and volume calculation in MRI images
(with B. Mansouri, M. Chetioui, L. Boumia, C. Zouaoui)
Numer. Multimed. Tools Appl. (2025), vol. 84, 8745--8766, doi

Optimal control of lake eutrophication
(with E. Comte)
J. Math. Anal. Appl. (2023), vol. 528, no. 2, 127728 doi

A numerical scheme for the optimal control of groundwater pollution
(with M.M. Diédhiou, H. Nasser El Dine, C. Saint-Jean)
Numer. Methods Partial Differ. Equ. (2023), vol. 39(4), 3037--3063, doi

A game theory approach for the groundwater pollution control
(with E. Augeraud-Véron, É. Comte, M.M. Diédhiou)
SIAM J. Control Optim. (2022), vol. 60(3), doi

Homogenization results for a Landau-Lifshitz-Gilbert equation in composite materials with transmission defects
(with M. Ouhadan, M. Tilioua)
Applicable Analysis (2022), vol. 101(12), 4126--4148, doi

Well-posedness of general cross-diffusion systems
(with C. Rosier, L. Rosier)
J. of Diff. Equations (2021), vol. 300, 386--425, doi

A companion paper for Well-posedness of general cross-diffusion systems:  
arXiv (2021), arXiv:2108.13221, 16 pp., link

Optimal buffer zone for the control of groundwater pollution from agricultural activities
(with E. Augeraud-Véron, É. Comte).
Applied Mathematics and Optimization (2020), vol. 84(1), 51--83, doi

Modelling of shallow aquifers in interaction with overland water
(with C. Bourel, C. Rosier, M. Tsegmid).
Applied Mathematical Modelling (2020), vol. 81, 727--751.

Fully automatic multi segmentation approach for MRI brain tumor detection using improved region growing and QMC-EM algorithm
(with H. Belkacem, Z. Chama, F. Alim-Ferhat, L. El Seddik, A. Abderrahmane, M. Anani).
International Journal of Imaging Systems and Technology (2020), vol. 30 (1), 104--111.

Derivation of Feynman-Kac and Bloch-Torrey equations in a trapping medium
(with M.C. Néel).
Methodology and Computing in Applied Probability (2020), vol. 22, 49--74. 

Existence, uniqueness and asymptotic analysis of optimal control problems for a model of groundwater pollution
(with E. Augeraud, E. Comte).
ESAIM: COCV (2019), vol. 25 (53), doi

Homogenization of the Landau-Lifshitz-Gilbert equation in a contrasted composite medium
(with M. Moumni, M. Tilioua).
Discrete and Continuous Dynamical Systems-S (2018), vol. 11 (1), 35--57.

Uniqueness for cross-diffusion systems issuing from seawater intrusion problems (with J. Li, C. Rosier).
Electr. J. of Diff. Equations (2017), vol. 2017 (256), 1--22.

Mathematical analysis of a seawater intrusion model including storativity
(with M.M. Diédhiou, C. Rosier).
SIAM J. of Math. Anal. (2017), vol. 49 (1), 29--63.

Numerical validation of an upscaled sharp-diffuse interface model for stratified miscible flows
(with L. Cherfils, M.M. Diédhiou).
Mathematics and Computers in Simulation, (2017), vol. 137, 246--265.

Optimal control for a groundwater pollution ruled by a convection-diffusion-reaction problem (with E. Augeraud, E. Comte)
JOTA, J. of Optimization Theory and Applications, (2017), vol. 173, 941--966.

Derivation of a sharp-diffuse interfaces model for seawater intrusion in a free aquifer. Numerical simulations (with M.M. Diédhiou, C. Rosier).
SIAM J. of Appl. Math. (2016), vol. 76 (1), 138--158.

Mathematical analysis of a sharp-diffuse interfaces model for seawater intrusion (with M.M. Diédhiou, C. Rosier).
J. of Diff. Equations (2015), vol. 259 (8), 3803--3824.

Global existence for seawater intrusion models: comparison between sharp interface and sharp-diffuse interface approaches (with J. Li, C. Rosier).
Electr. J. of Diff. Equations, (2015), vol. 2015 (126), 1--27.

From particles scale to anomalous or classical convection-diffusion models with path integrals
(with M.C. Néel).
DCDS, (2014), vol. 7(2) 207--238.

Effective models for reactive flow under dominant Péclet and Damköhler numbers: numerical simulations
(with C. Rosier).
Nonlinear Analysis RWA, (2014), vol. 15, 345--360.

Roughness-induced effect at main order on the Reynolds approximation
(with D. Bresch, L. Chupin, Th. Colin, and M. Gisclon).
SIAM Multiscale Model. Simul., (2010), vol. 8(3), 997--1017 & erratum.

Parabolic and degenerate parabolic models for pressure-driven transport problems.
Math. Models Meth. App. Sci., (2010), vol. 1(4), 1--24.

Homogenization of a class of quasilinear elliptic equations with non–standard growth in high-contrast media
(with L. Pankratov).
Proc. Roy. Soc. Edinburgh Sect. A, (2010), vol. 140, 495--539.

Analysis of a finite volume-finite element scheme for a nuclear transport model
(with S. Zimmermann).
IMA J. Num. Anal.15 (2009), 1--30.

Nonlinear double porosity models with non-standard growth
(with L. Pankratov).
C.R. Mecanique, (2009), no. 337, 659--666.

Rigorous upscaling of the reactive flow with finite kinetics and under dominant Peclet number
(with A. Mikelic).
Continuum Mechanics and Thermodynamics, (2009), vol. 21, 125--140.

Homogenization of a model of transport of heat and mass
(with A. Sili).
Networks and Heterogeneous Media 4 (2009), no. 4, 649--666.

Asymptotic analysis of a radionuclide transport model with unbounded viscosity.
Advanced Nonlinear Studies 9 (2009), 227--241.

Homogenized model for flow in partially fractured media.
Electronic J. Diff. Equations 2009 (2009), no. 1, 1--27.

Asymptotic analysis of a nonlinear parabolic problem modelling miscible compressible displacement in porous media.
NoDEA, Nonlinear Differential Equations and Appl.15 (2008), no. 6, 757--782.

Laplace transform approach to the rigorous upscaling of the infinite adsorption rate reactive flow under dominant Peclet number through a pore
(with A. Mikelic).
Appl. Anal. 87 (2008), no. 12, 1373--1395.

Mathematical analysis of a transport model with unbounded heat capacities.
Acta Appl. Math. 103 (2008), no. 3, 277--299.

Nuclear contamination in a naturally fractured porous medium
Int. J. of Pure and Applied Math. 42 (2008), no. 2, 281--288.

On a fully nonlinear parabolic problem modelling miscible compressible displacement in porous media.
J. Math. Anal. Appl. (2008), no. 339, 1112--1133.

Transport of heat and mass in a fluid with vanishing mobility.
Quart. Appl. Math. 66 (2008), no. 4, 771--779.

Semi-classical solutions for a nonlinear coupled elliptic-parabolic problem.
Bull. Austral. Math. Soc., (2007), no. 76, 369--396.

Derivation of models of compressible miscible displacement in partially fractured reservoirs.
Electronic J. Diff. Equations, (2007) no. 97, 1--29.

On a nonlinear parabolic system modelling miscible compressible displacement in porous media.
Nonlinear Anal. T.M.A. (2005) 6, no. 1-2, 237--260.

Radionuclide transport model with wells.
Asymptot. Anal. (2004) 37, no. 1, 57--78.

Existence result for a radionuclide transport model with unbounded viscosity.
J. Math. Fluid Mech. (2004) 6, no. 4, 365--388.

Derivation of the double porosity model of a compressible miscible displacement in naturally fractured reservoirs.
Appl. Anal. (2004) 83, no. 5, 477--499.

Homogenization of a one-dimensional model for compressible miscible flow in porous media.
Boll. Unione Mat. Ital. Sez. B. (2003) 6, no. 2, 399--414.

Proceedings

On a compressible miscible displacement in naturally fractured reservoirs.
2nd Biot Conference on Poromechanics, A.A. Balkema, Rotterdam , (2002), 8 pp.

Roughness-Induced Effect on the Reynolds Approximation
(with L. Chupin, M. Gisclon).
ICNAAM 2009, 7th International Conference of Numerical Analysis and Applied Mathematics, (2009), 7 pp.

Feynman-Kac equation for convection, dispersion and sorption
(with M.C. Néel).
Chaos Complexity and Transport, World Scientific (2012), 9 pp.

Numerical analysis of a finite volume scheme for the optimal control of groundwater pollution
(with M.M. Diédhiou, H. Nasser El Dine)
Finite Volumes for complex applications 9, Springer Proceedings in Mathematics and Statistics (2020), 10 pp.

Preprints