Short bio

Since 2021, I am assistant profressor (maître de conférence) at the Université de Technologies de Compiègne. I am a member of the EPIA team of the Laboratoire de Mathémtiques Appliquées de Compiègne (LMAC). From September 2024 to February 2025, I was in délégation CNRS at the IRL CRM CNRS of the Université de Montréal.

From October 2019 to July 2021 I was a postdoc at the Technische Universität of Vienna. I worked in Ansgar Jüngel team. I defended my PhD on 26th September 2019 at the Laboratoire Paul Painlevé of the Université de Lille. I did my PhD under the supervision of Claire Chainais-Hillairet and Benoît Merlet.

You can find here (in french) my Curriculum Vitæ.

Research interests

I am mainly interested by the theoretical and numerical analysis of PDEs.

Keywords: Analysis of PDEs, numerical analysis, system of parabolic equations, free boundary problems, cross-diffusion systems, finite volume schemes, nonlocal transport equations, entropy method, calculus of variations, computer assisted proof.

Orcid Id: https://orcid.org/0000-0003-2556-4577

PhD students

I am currently co-supervising two PhD students:

- Diana Al Zareef, since October 2023, with A. El Hajj and H. Ibrahim.

- Mohamad El Hajj Chehade, since October 2024, with A. El Hajj .

Preprints

Constructive existence proofs and stability of stationary solutions to parabolic PDEs using Gegenbauer polynomials , with M. Breden and M. Cadiot , submitted for publication, 2026.

Analysis of a degenerate parabolic system for cell dynamics in intestinal crypts, with A. El Hajj and M. El Hajj Chehade, submitted for publication, 2026.

Convergence of a scheme for a two dimensional nonlocal system of transport equations, with D. Al Zareef and A. El Hajj , submitted for publication, 2026.

Analysis of a one dimensional energy dissipating free boundary model with nonlinear boundary conditions. Existence of weak solutions, with B. Merlet and J. Venel, submitted for publication, 2025.

A nonlocal regularization of a generalized Busenberg-Travis cross-diffusion system, with A. Jüngel and M. Vetter, submitted for publication, 2024.

Articles

A finite volume scheme for the local sensing chemotaxis model, with M. Herda and A. Trescases. SMAI Journal of Computational mathematics, vol. 11, pp. 637-676, 2025.

Convergence of a semi-explicit scheme for a one dimensional periodic nonlocal eikonal equation modeling dislocation dynamics, with D. Al Zareef, A. El Hajj and H. Ibrahim. ESAIM: M2AN, vol. 59, no. 6, 2957-2990, 2025.

A convergent finite-volume scheme for nonlocal cross-diffusion systems for multi-species populations, with A. Jüngel and S. Portisch. ESAIM: M2AN, vol. 58, no. 2, 759-792, 2024.

Study of an entropy dissipating finite volume scheme for a nonlocal cross-diffusion system, with M. Herda. ESAIM: M2AN, vol. 57, no. 3, 1589-1617, 2023. The codes associated to this work can be found here.

Analysis of a finite-volume scheme for a single-species biofilm model, with C. Helmer and A. Jüngel. Appl. Numer. Math. 185, 386—405, 2022.

Nonlocal cross-diffusion systems for multi-species populations and networks, with A. Jüngel and S. Portisch. Nonlin. Anal. 219, no. 112800, 26 pages, 2022.

A convergent finite volume scheme for dissipation driven models with volume filling constraint, with C. Cancès. Numer. Math. 151, 279–328, 2022.

A discrete boundedness-by-entropy method for finite-volume approximations of cross-diffusion systems, with A. Jüngel. IMA J. Numer. Anal. 43, 560–589, 2023.

Existence of traveling waves solutions for the Diffusion Poisson Coupled Model: a computer-assisted proof, with M. Breden and C. Chainais-Hillairet. ESAIM: M2AN, vol. 55, no. 4, 1669–1697, 2021. The codes associated to this work can be found here.

A convergent structure-preserving finite-volume scheme for the Shigesada-Kawasaki-Teramoto population system, with A. Jüngel. SIAM J. Numer. Anal., 59, 2286-2309, 2021.

Convergence of a finite-volume scheme for a degenerate-singular cross-diffusion system for biofilms, with E. S. Daus and A. Jüngel. IMA J. Numer. Anal., 2020.

Numerical approximation of a concrete carbonation model: Study of the √t-law of propagation. Numer. Methods Partial Differential Eq., 1-20, 2019

Convergence of a finite volume scheme for a parabolic system with a free boundary modeling concrete carbonation, with C. Chainais-Hillairet and B. Merlet. ESAIM: M2AN, vol. 52, no. 2, 457-480, 2018.

Proceedings

A finite-volume scheme for a cross-diffusion model arising from interacting many-particle population systems, with A. Jüngel.
FVCA9 -International Conference on Finite Volumes for Complex Applications IX, Bergen, Norway, 2020.

Design and analysis of a finite volume scheme for a concrete carbonation model, with C. Chainais-Hillairet and B. Merlet.
Springer International Publishing, 285-292, 2017.

Memoirs

Free boundary problems for the degradation of materials and biofilms growth: numerical analysis and modelisation. PhD Thesis, Université de Lille, 2019.

Lecture Notes

You can find here (in french) my lecture notes on Fourier series and Fourier transform intended for engineering students. Despite numerous revisions, if you find any mistakes, please let me know!