Publications

Memoirs, Reviews and Summer schools

Introduction to my PhD thesis.
Habilitation.
Averaging Lemmas (Porto Ecrole 2008 and Granada 2009) together with slides of the course.
Mean field limits (Granada 2008) and the proceedings of a similar course in Les Houches 2008.
A review of the Mean-Field limits for Vlasov equations, Kinet. Relat. Models 7 (2014), 661-711.
A review of Mean-Field limit for Stochastic Particle Systems. Active Particles, Volume 1: Theory, Models, Applications, Birkhauser-Springer (Boston), series Modelling and Simulation in Science Engineering and Technology.

P.-E. Jabin, D. Bresch, Z. Wang, Mean-field limit and quantitative estimates with singular attractive kernels. Preprint.
P.-E. Jabin, H.-Y. Lin, E. Tadmor, A new commutator method for averaging lemmas. Séminaire Laurent Schwartz – EDP et applications.
W. Fagan, P.-E. Jabin, H.-Y. Lin, Memory-driven movement model for periodic migrations. To appear Journal of Theoretical Biology.
P.-E. Jabin, H.-Y. Lin, E. Tadmor, Commutator Method for Averaging Lemmas. arXiv:2003.05047.
W. Czaja, D. Dong, P.-E. Jabin, F.O.N. Njeunje, Analysis of hyperspectral data by means of transport models and machine learning. Accepted in IGARSS 2020.
L. Berlyand, P.-E. Jabin, C. A. Safsten, Stability for the Training of Deep Neural Networks and Other Classifiers. Preprint.
D. Bresch, P.-E. Jabin, Z. Wang, Modulated free energy and mean field limit. Séminaire Laurent Schwartz – EDP et applications.
P.-E. Jabin, A. Mellet, M. Molina, Optimal transportation in a discrete setting. arXiv:1911.00574.
W. Czaja, D. Dong, P.-E. Jabin, F.O.N. Njeunje, Transport Model for Feature Extraction. To appear SIMODS.
D. Bresch, P.-E. Jabin, Z. Wang. On Mean Field Limit and Quantitative Estimates with a Large Class of Singular Kernels: Application to the Patlak-Keller-Segel Model. Comptes rendus – Mathématique, 357 (2019), no. 9, 709-720. DOI: 10.1016/j.crma.2019.09.007.
L. Berlyand, P.-E. Jabin, M. Potomkin, E. Ratajczyk. A kinetic approach to active rods dynamics in confined domains. Multiscale Model. Simul. 18-1 (2020), 1-20, DOI: 10.1137/19M1263510.
D. Bresch, P.-E. Jabin, Viscous compressible flows under pressure. Fluids under Pressure, Birkhäuser Publishing Ltd.
J. Zhu, S. Teolis, N. Biassou, A. Tabb, P-E Jabin, O. Lavi. Tracking the adaptation and compensation processes of patients’ brain arterial network to an evolving glioblastoma. To appear Transactions on Pattern Analysis and Machine Intelligence.
J. Calvo, P.-E. Jabin, J. Soler, Global weak solutions to the relativistic BGK equation. Comm. Partial Differential Equations, 45 (2020), no. 3, 191–229.
W. Cai, P.-E. Jabin, H. Liu, Time-asymptotic Convergence Rates towards discrete steady states of a nonlocal selection-mutation model. Math. Models Methods Appl. Sci. 29 (2019), no. 11, 2063–2087.
L. Berlyand, R. Creese, P.-E. Jabin, M. Potomkin, Continuum approximations to systems of correlated interacting particles. J. Stat. Phys. 174 (2019), no. 4, 808–829.
L. Berlyand, P.-E. Jabin, On the convergence of formally diverging neural net-based classifiers. Comptes rendus – Mathématique, 356 (4), 2018 395–405, DOI: 10.1016/j.crma.2018.03.003.
D. Bresch, P.-E. Jabin, Quantitative estimates for advective equations with degenerate anelastic constraint. Proceedings of the International Congress of Mathematicians—Rio de Janeiro 2018. Vol. III. Invited lectures, 2167–2192, World Sci. Publ., Hackensack, NJ, 2018.
P.E. Jabin, Z. Wang, Quantitative estimates of propagation of chaos for stochastic systems with W^{-1,\infty} kernels. Inventiones Matematicae 214 (2018), no. 1, 523-591.
D. Bresch, P.E. Jabin, Global Existence for Navier-Stokes Equations for thermodynamically unstable pressure and anisotropic viscous stress. Annals Math. 188} (2018), no. 2, 577-684.
D. Bresch, P.-E. Jabin, Quantitative regularity estimates for compressible transport equations. New trends and results in mathematical description of fluid flows, 77–113, Necas Center Ser., Birkhäuser/Springer, Cham, 2018.
P. Castelli, P.E. Jabin, S. Junca, Fractional spaces and conservation laws. Theory, numerics and applications of hyperbolic problems. I, 285–293, Springer Proc. Math. Stat., 236, Springer, Cham, 2018.
P.E. Jabin, H. Liu, On a nonlocal selection-mutation model with a gradient flow structure. Nonlinearity 30 (2017), no. 11, 4220-4238.
F. Ben Belgacem, P.E. Jabin, Convergence of numerical approximations to non-linear continuity equations with rough force fields. Arch. Ration. Mech. Anal., 234 (2019), no. 2, 509–547. DOI 10.1007/s00205-019-01396-3.
P.-E. Jabin, R. Schram, Selection-Mutation dynamics with spatial dependence. To appear J. de Math. Pures et Appl.
D. Bresch, P.-E. Jabin, Global weak solutions of PDEs for compressible media: A compactness criterion to cover new physical situations. Springer INdAM-series, special issue dedicated to G. Métivier. Eds F. Colombini, D. Del Santo, D. Lannes, 33-54, (2017).
P.E. Jabin, T. Rey, Hydrodynamic Limit of Granular Gases to Pressureless Euler in Dimension 1. Quart. Appl. Math. 75 (2017), no. 1, 155-179.
P.-E. Jabin, Z. Wang, Mean Field limit and Propagation of Chaos for Vlasov Systems with Bounded Forces. J. Funct. Anal. 271 (2016), no. 12, 3588-3627.
P.E. Jabin, Critical non Sobolev regularity for continuity equations with rough force fields. J. Differential Equations 260 (2016), no. 5, 4739-4757.
P.E. Jabin, A. Miroshnikov, R. Young, Cellulose Biodegradation Models; An Example of Cooperative Behaviour in Structured Populations. ESAIM Math. Model. Numer. Anal. 51 (2017), no. 6, 2289-2318.
W. Cai, P.E. Jabin, H. Liu, Time-asymptotic Convergence Rates towards the Discrete Evolutionary Stable Distribution. Math. Models Methods Appl. Sci. 25 (2015), no. 8, 1589-1616.
P.E. Jabin, S. Junca, A continuous model for ratings. Siam J. Appl. Math 75 (2015), no. 2, 420-442.
L. Berlyand, P.E. Jabin, M. Potomkin, Complexity Reduction in many Particle Systems with Random Initial Data, SIAM Journal on Uncertainty Quantification 2016 4:1, 446-474.
N. Champagnat, P.E. Jabin, Strong solutions to stochastic differential equations with rough coefficients. Annals of Proba, 46 (2018), no. 3, 1498-1541.
P.E. Jabin, S. Motsch, Clustering and asymptotic behavior in opinion formation. J. Differential Equations 257 (2014), no. 11, 4165-4187.
Y. Bourgaut, D. Broizat, P.E. Jabin, Convergence rate for the method of moments with linear closure relations. Kinet. Relat. Models 8 (2015), no. 1, 1-27.
N. Champagnat, P.E. Jabin, S. Méléard, Adaptation in a stochastic multi-resources chemostat model. J. de Math. Pures et Appl. 9 101 (2014), no. 6, 755-788.
P.E. Jabin, N. Masmoudi, DiPerna-Lions flow for relativistic particles in an electromagnetic field. Arch. Ration. Mech. Anal. 215 (2015), no. 3, 1029–1067.
M. Hauray, P.E. Jabin, Particles approximations of Vlasov equations with singular forces : Propagation of chaos. Annal. Ecol. Norm. Sup. 48 (2015), no. 4, 891-940.
P.E. Jabin, Mathematical models for morphogenesis: Linear or non linear diffusion; Comment on “Morphogenetic action through flux-limited spreading” by Verbeni, Sánchez, Mollica, Siegl-Cachedenier, Carleton, Guerrero, Ruiz i Altaba, Soler. Physics of Life Reviews, Volume 10, 4-Oct-2013, 485-486.
M. Bossy, J. Fontbona, P.E. Jabin, J.F. Jabir, Local existence of analytical solutions to an incompressible Lagrangian stochastic model in a periodic domain. Comm. Partial Diff. Eq. 38, Issue 7, July 2013, 1141-1182.
P.E. Jabin, Small populations corrections for selection-mutation models. Netw. Heterog. Media 7 (2012), no. 4, 805-836.
F. Ben Belgacem, P.E. Jabin, Compactness for nonlinear continuity equations. J. Funct. Anal. 264 (2013), no. 1, 139–168.
P.E. Jabin, A. Nouri, Analytic solutions to a strongly nonlinear Vlasov equation. C.R. Acad. Sci. Paris Ser. I Math., 349 (2011), no. 9-10, 541-546.
N. Champagnat, P.E. Jabin, The evolutionary limit for models of populations interacting competitively with many resources. J. Diff. Eq. 251 (2011), no. 1, 176-195.
P.E. Jabin, G. Raoul, Long time asymptotics for selection dynamics. J. Math. biol. 63 (2011), no. 3, 493-517.
J. Calvo, P.E. Jabin, Large time asymptotics for a modified coagulation models. J. Differential Equations 250 (2011), no. 6, 2807-2837.
N. Champagnat, P.E. Jabin, G. Raoul, Convergence to equilibrium in competitive Lotka-Volterra and chemostat systems. C.R. Math. Acad. Sci. Paris 348 (2010), no. 23-24, 1267-1272.
A. Gerschenfeld, P.E. Jabin, The mean-field limit for interacting particles. Long-range interacting systems 14, 320-328, Oxford Univ. Press, Oxford, 2010.
J. Barré, M. Hauray, P.E. Jabin, Quantitative stability estimates for systems of many interacting particles. J. Stat. Mech., (2010), doi:10.1088/1742-5468/2010/07/P07005.
N. Champagnat, P.E. Jabin, Well posedness in any dimension for some Hamiltonian flows with non BV force terms. Comm. Partial Diff. Eq. 35 (2010), no. 5, 786-816.
P.E. Jabin, Differential Equations with singular fields. J. de Math. Pures Appl. (9) 94 (2010), no. 6, 597-621.
P.E. Jabin, Some regularizing methods for transport equations and the regularity of solutions to scalar conservation laws. Séminaire: Equations aux Dérivées Partielles, 2008-2009, Exp. No. XVI, 15 pp., Sémin. Equ. Dériv. Partielles, Ecole Polytech., Palaiseau.
P.E. Jabin, J. Soler, A coupled Boltzmann & Navier-Stokes fragmentation model induced by a fluid-particle-spring interaction. Simul. 8 (2010), 1244-1268.
I. Brazzoli, E. De Angelis, P.E. Jabin, A Mathematical Model of Immune Competition Related to Cancer Dynamics. Math. Model. Methods Appl. Sci. 33 (2010), 733-650.
A. Habbal, P.E. Jabin, Two short presentations related to cancer modeling. ARIMA Rev. Afr. Rech. Inform. Math. Appl. 10 (2008-2009).
P.E. Jabin, Averaging Lemmas and Dispersion Estimates for kinetic equations. Riv. Mat. Univ. Parma 1 (2009), 71-138.
P.E. Jabin, A. Tzavaras, Kinetic decomposition for periodic homogenization problems. Siam J. Math. Anal. 41 (2009), 360-390.
P.E. Jabin, V. Lemesle, D. Aurelle, A continuous size-structured red coral growth model. Math. Models Methods Appl. Sci., 18 (2008), no. 11, 1927-1944.
L. Desvillettes, P.E. Jabin, S. Mischler, G. Raoul, On selection dynamics for continuous structured populations. Commun. Math. Sci. 6 (2008), no. 3, 729-747.
J. Barré, P.E. Jabin, Free transport limit for N-particles dynamics with singular and short range potential. J. Stat. Phys. 131 (2008), no. 6, 1085-1101.
L. Derbel, P.E. Jabin, The set of concentration for some hyperbolic models of chemotaxis. J. Hyperbolic Differ. Equ. 4 (2007), no. 2,
331-349.
M. Hauray, P.E. Jabin, N-particles approximation of the Vlasov-Poisson equation with singular potentials. Arch. Ration. Mech. Anal., 183 (2007), no. 3, 489-524.
P.E. Jabin, J. Soler, A Kinetic Description of Particle Fragmentations. Math. Methods Appl. Sci. 16, 933-948 (2006).
C. Baranger, L. Boudin, P.E. Jabin, S. Mancini, A modeling of biospray for the upper airways. CEMRACS 2004-mathematics and
applications to biology and medicine, 41-47 (electronic), ESAIM Proc., 14, EDP Sci., 2005.
E. De Angelis, P.E. Jabin, Mathematical Models of Therapeutical Actions Related to Tumour and Immune System Competition. Math. Methods Appl. Sci. 28, no. 17, 2061-2083 (2005).
O. Diekmann, P.E. Jabin, S. Mischler and B. Perthame, The dynamics of adaptation : an illuminating example and a Hamilton-Jacobi approach. Th. Pop. Biol. 67, 257-271 (2005).
C. Klingenberg, P.E. Jabin, Existence of solutions to an inhomogeneous, kinetic model of droplet coalescence. Nonlinear partial differential equations and related analysis, 181-192, Contemp. Math., 371, Amer. Math. Soc., Providence, RI, 2005.
P.E. Jabin, L. Vega, A Real Space Method for Averaging Lemmas. J. de Math. Pures et Appl. 83, 1309-1351 (2004).
T. Goudon, P.E. Jabin and A. Vasseur, Hydrodynamic limits for Vlasov-Stokes equations: Part II: Fine Particles Regime. Indiana Univ. Math. J. 53, 1517-1536 (2004).
T. Goudon, P.E. Jabin and A. Vasseur, Hydrodynamic limits for Vlasov-Stokes equations: Part I: Light Particles Regime. Indiana Univ. Math. J. 53, 1495-1513 (2004).
P.E. Jabin, L. Vega, Lemmes de moyenne et Transformée aux rayons X. C.R. Acad. Sci. Paris Sér. I Math. 337, 505-510 (2003).
H. Frid, P.E. Jabin, B. Perthame, Global Stability of Steady Solutions for a Model in Virus Dynamics. Math. Model. Numer. Anal. 37, 709-723 (2003).
P.E. Jabin, B. Niethammer, On the rate of convergence to equilibrium in the Becker-Döring equations. J. Differential Equations 191, 518-543 (2003).
P.E. Jabin, B. Perthame, Kinetic methods for Line-energy Ginzburg-Landau models. Séminaire sur les Equations aux Dérivées Partielles, 2001-2002, Exposé XIII, Ecole Polytech., Palaiseau, 2002.
E. De Angelis, P.E. Jabin, Qualitative Analysis of a Mean Field Model of Tumor-Immune System Competition. Math. Models Methods Appl. Sci. 13, 187-206 (2003).
P.E. Jabin, B. Perthame, Regularity in kinetic formulations via averaging lemmas. ESAIM Control Optim. Calc. Var. 8, 761-774 (2002).
P.E. Jabin, F. Otto and B. Perthame, Line-energy Ginzburg-Landau models: zero-energy states. Ann. Sc. Norm. Sup. Pisa 5, 187-202 (2002).
P.E. Jabin, Various levels of models for aerosols, Math. Models Methods Appl. Sci. 12, 903-919 (2002).
P.E. Jabin, B. Perthame, Compactness in Ginzburg-Landau energy by kinetic averaging. Comm. Pure Appl. Math. 54, 1096-1109 (2001).
P.E. Jabin, B. Perthame, Compacité par lemmes de moyenne cinétiques pour des énergies de Ginzburg-Landau. C.R. Acad. Sci. Paris Sér. I Math. 331}, 441-445 (2000).
P.E. Jabin, F. Otto, Identification of the dilute regime in particle sedimentation. Comm. Math. Phys. 250, 415-432 (2004).
P.E. Jabin, The Vlasov-Poisson system with infinite mass and energy. J. Statist. Phys. 103, 1107-1123 (2001).
I. Gasser, P.E. Jabin and B. Perthame, Regularity and propagation of moments in some nonlinear Vlasov systems. Proc. Roy.
Soc. Edinburgh Sect. A 130, 1259-1273 (2000).
P.E. Jabin, Macroscopic limit of Vlasov type equations with friction. Ann. Inst. H. Poincaré Anal. Non Linéaire 17, 651-672 (2000).
P.E. Jabin, B. Perthame, Notes on mathematical problems on the dynamics of dispersed particles interacting through a fluid. Modelling in applied sciences, a kinetic theory approach, 111-147, Model. Simul. Sci. Eng. Technol., Birkhauser Boston, 2000.
P.E. Jabin, Large time concentrations for solutions to kinetic equations with energy dissipation. Comm. Partial Differential Equations 25, 541-557 (2000).