Publications

Articles accéptés

1. T. Goudon, F. Lagoutière, L. Tine. The Lifschitz-Slyozov equation with space-diffusion of monomers: Kinet. Relat. Models 5 (2012), no.2, 325--355.
2. T. Goudon, F. Lagoutière, L. Tine. Simulations of the Lifschitz-Slyozov equations: the role of the coagulation term in the asymtotic behavior: M3AS. (2012), Vol.23, no.7, 1177-1215.
3. M. Doumic, L. Tine. Estimating the Division Rate for the Growth-Fragmentation Equation: J. Math. Biol., Vol.67, no.1 (2012), pp. 69-103.
4. 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.
5. 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.
6. P. Gabriel, L. Tine High-order WENO scheme for polymerization-type equations : ESAIM Proc., Vol.30 (2010), p.54-70.
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).

Articles soumis

1. I. Ciuperca, L. Pujo-Menjouet, L. M. Tine, N. Torres, V. Volpert A qualitative analysis of a Aβ-monomer model with inflammation processes for Alzheimer's disease : To appear in PLOS ONE.
2. T. Chen, C. Yang, L. M. Tine, Z. Guo A new collision avoidance model with random batch resolution strategy : To appear in JCP.

Articles en préparation

1. With N. Meunier. A Mathematical Model for the Growth of Atherosclerotic plaque in a population of rabbits under lipid-rich diet.
2. With J. Dambrine, N. Meunier. Évolution et Influence du taux de Cisaillement dans un écoulement artériel à géométrie déformée.
3. With B. Maury. Finit Element 3D Simulation of the Navier-Stokes Equations: Shear Stress reconstruction.

Chapitre d'ouvrage

1. With B. leye and M. Sy. Optimal control of thermal pollutionemitted by power plants
   À paraître dans le livre Numerical Simulation, IntechOpen.

Thèse

Titre: Analyse mathématique et numérique de modèles de coagulation-fragmentation
Thèse soutenue le 9 Décembre 2011, effectuée sous la direction de Thierry Goudon, Frédéric Lagoutière et Mamadou Sy .