Publications

Articles accéptés et preprints

1. P. Gabriel, L. Tine High-order WENO scheme for polymerization-type equations : ESAIM Proc., Vol.30 (2010), p.54-70.
2. T. Goudon, F. Lagoutière, L. Tine. The Lifschitz-Slyozov equation with space-diffusion of monomers: Kinet. Relat. Models 5 (2012), no.2, 325--355.
3. S. Prigent, A. Ballesta, F. Charles, P. Gabriel, L. Tine, H. Rezaei, M. Doumic. An Efficient Kinetic Model for Assemblies of Amyloid Fibrils and Its Application to Polyglutamine Aggregation: PloS One. (2012), Vol.7, no.11.
4. M. Doumic, L. Tine. Estimating the Division Rate for the Growth-Fragmentation Equation: J. Math. Biol., Vol.67, no.1 (2012), pp. 69-103.
5. T. Goudon, F. Lagoutière, L. Tine. Simulations of the Lifschitz-Slyozov equations: the role of the coagulation term in the asymtotic behavior: M3AS. (2013), Vol.23, no.7, 1177-1215.
6. T. Goudon, M. Sy, L. Tine. A FLUID-KINETIC MODEL FOR PARTICULATE FLOWS WITH COAGULATION AND BREAKUP: STATIONARY SOLUTIONS, STABILITY AND HYDRODYNAMIC REGIMES : SIAM J. APPL. MATH. Vol.73, no.1 (2013) pp. 401-421.
7. Ben M. Dia, A. Diagne, L. Tine A generalized finite difference method for 2-D nonlinear shallow water equations: CARI'14 Proc., Vol. 12 (2014), pp. 81-88.
8. L. Tine Inverse problem for cell division rate in population dynamics: ITM Web of Conferences 4, 01003 (2015). DOI: 10.1051/itmconf/20150401003. EDP Sciences, (2015).
9. C. Yang, L. Tine A hybrid finite volume method for advection equations and its applications in population dynamics: Numerical Methods for Partial Differential Equations, Wiley (2016). DOI: 10.1002/num.22134 .
10. M. Helal, A. Igel-Egalon, A. Lakmeche, P. Mazzocco, A. Perrillat-Mercerot, L. Pujo-Menjouet, H. Rezaei, L. Tine Stability analysis of a steady state of a model describing Alzheimer's disease and interactions with prion proteins.: Journal of Mathematical Biology, 2018, DOI: 10.1007/s00285-018-1267-1, (2018).
11. B. Leye, L. Tine Analysis and Numerical Simulation of a Polymerization Model with Possible Agglomeration Process.: Acta Applicandae Mathematicae (ACAP), (2018). DOI: 10.1007/s10440-018-0222-x .
12. I. Ciuperca, M. Dumont, A. Lakmeche, P. Mazzocco, L. Pujot-Menjouet, H. Rezaei, L. Tine Alzheimer's disease and prion: an in vitro mathematical model : DCDS-B, 24(10): 5225-5260. doi: 10.3934/dcdsb.2019057, October 2019 .
13. M. Caléro, I. S. Ciuperca, L. Pujot-Menjouet, L. M. Tine Alzheimer disease: Convergence Result from a Discrete Model Towards a Continuous One : Springer Nature Switzerland, Trends in biomathematics, 2019.
14. J. Jaouad, K. Allali, L. M. Tine, V. Volpert Nonlinear spatio-temporal viral infection model with CTL immunity: Mathematical analysis : Mathematics/Special Issues/The Application of Mathematics to Physics and Nonlinear Science, December, 2019 .
15. M. Andrade-Restrepo, P. Lemarre, I. Ciuperca, L. Pujot-Menjouet, L. M. Tine Modeling the spatial propagation of Aβ oligomers in Alzheimer's Disease : ESAIM: ProcS, Numerical and mathematical modeling for biological and medical applications:deterministic, probabilistic and statistical descriptions, Vol. 67: 30--45, DOI: 10.1051/proc/202067003, (2020).
16. C. Yang, L. M. Tine Analysis and Numerical Simulations of a Reaction-Diffusion Model with fixed Active Bodies : SIAM Journal on Applied Mathematics, Vol. 81 (4), DOI: 10.1137/20M1343385, (2021).
17. M. S. Goudiaby, A. Diagne, L. M. Tine Longtime behavior of a second order finite element scheme simulating the kinematic effects in liquid crystal dynamics : CPAA Communications on Pure and Applied Analysis, Vol. 20 (10):3499--3514, DOI: 10.3934/cpaa.2021116, (2021).
18. M. Andrade-Restrepo, I. Ciuperca, P. Lemarre, L. Pujot-Menjouet, L. M. Tine A reaction–diffusion model of spatial propagation of A𝛽 oligomers in early stage Alzheimer’s disease : Springer: Journal of Mathematical Biology, Vol. 82 (39), DOI:10.1007/s00285-021-01593-3, (2021).
19. C. Gueye, S. Ciuperca, L. Pujo-Menjouet, L. M. Tine Q-well-posedness of an Aβ-protein polymerization model : MMNP journal, Vol. 19, DOI: https://doi.org/10.1051/mmnp/2023028, (2024).
20. I. Ciuperca, L. Pujo-Menjouet, L. M. Tine, N. Torres, V. Volpert A qualitative analysis of an Aβ-monomer model with inflammation processes for Alzheimer's desease : Royal Society Open Science, DOI : 10.1098/rsos.231536, (2024).
21. K. Idhammou, J. El Karkri, R. Aboulaich, L. M. Tine Physics-informed neural networks for parameter estimation and simulation of a two-group epidemiological model : International Journal of Modeling, Simulation, and Scientific Computing, DOI: 10.1142/S1793962324500429, (2024).
22. I. S. Ciuperca, M. Mahjoub, L. M. Tine Aβ-protein polymerization in Alzheimer disease : Optimal control for nucleation parameter estimation : Journal of Theoretical Biology, 589, DOI: https://doi.org/10.1016/j.jtbi.2024.111814, (2024).
23. T. Chen, C. Yang, L. M. Tine, Z. Guo A new collision avoidance model with semi implicit random batch resolution : Communications in Mathematical Sciences, Vol 23(1), DOI: 10.4310/CMS.241217012958, (2025).
24. El Hajj, W., Pujo-Menjouet, L., Tine, L. M., Volpert, V. Modelling of anti-inflammatory treatment in Alzheimer disease: optimal regimen and outcome : Bulletin of Mathematical Biology, Vol. 87(12), (2025). DOI: https://doi:10.1007/s11538-025-01553-8, (2025).
25. K. Khalil, I. Mikiela, L. M. Tine Analysis and numerical simulations of a nonlocal advection-diffusion-reaction model for a population under stress : soumis au J. Physical Review E.
26. K. Idhammou Ouyoussef, J. El Karkri, L. M. Tine, R. Aboulaich Failure-informed PINN-based simulation of a multistrain epidemiological model : soumis au International Journal of Applied Mathematics.

Chapitre d'ouvrage

1. With B. leye and M. Sy. Optimal control of thermal pollution emitted by power plants
   Numerical Simulation, IntechOpen (2019).

HDR et Thèse

1. Titre Thèse: Analyse mathématique et numérique de modèles de coagulation-fragmentation. Thèse soutenue le 9 Décembre 2011.
   
2. Titre HDR: Contribution à la modélisation mathématique et au calcul scientifique: Dynamique de population, Modèles structurés pour la maladie d'Alzheimer, Schéma numériques, Problèmes inverses et Contrôle optimal pour l'estimation de paramètres
   HDR soutenue le 9 janvier 2025 à l'Université Lyon 1.