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, entropy method, calculus of variations, computer assisted proof.
Orcid Id: https://orcid.org/0000-0003-2556-4577
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, submitted for publication, 2025.
A finite volume scheme for the local sensing chemotaxis model, with M. Herda and A. Trescases, submitted for publication, 2024.
A nonlocal regularization of a generalized Busenberg-Travis cross-diffusion system, with A. Jüngel and M. Vetter, submitted for publication, 2024.
Analysis of a one dimensional energy dissipating free boundary model with nonlinear boundary conditions. Existence of global weak solutions, with B. Merlet and J. Venel, submitted for publication, 2022.
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.
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.
Free boundary problems for the degradation of materials and biofilms growth: numerical analysis and modelisation.
PhD Thesis, Université de Lille, 2019.