Update :  May 2014


Laboratoire J.-L. Lions

Université Pierre et Marie Curie
 4, pl. Jussieu
75252 Paris cedex 05
Tour 16-26, etage 3,  bureau 325
tel.   (33) 1 44 27  85 18
sec.   (33) 1 44  27 42 98
Email :  Benoit.Perthame’at’


INRIA projet MAMBA                                        Mastere M2:  "Mathématiques appliquées aux sciences biologiques et biomédicales"

Some lecture notes

Research topics



Motion of cells and chemotaxis:    Parabolic, hyperbolic and kinetic models are used to describe the collective motion and self-organization of cells or bacterial colonies.


Population balance laws:     Growth in cell populations, polymerization processes by aggregation and fragmentation. The inverse problem is particularly interesting.


Motivated by darwinian evolution : Multiplication, selection and mutations are principles that can be written in nonlocal parabolic models.

They give rise to solutions that concentrate as Dirac masses.


PDE models for neuronal networks :    Closure of stochastic models of neuronal networks lead to interesting PDE models as the Integrate and Fire or Elapsed Time model.

Questions here are to understand desynchronsation, spontaneous activity, information coding.


Tumor growth and resistance to chemotherapy :    This is an ongoing project in the team   MAMBA


Renal flows :     This is an ongoing project with :  A. Edwards (CNRS-INSERM, ERL 7226 - UMRS 872),  N. Seguin and M. Tournus


Other topics


A short-vitae                              Bibliography (recent papers)



                                                                                                         Recent preprints


Derivation of a Hele-Shaw type system from a cell model with active motion with F. Quiros, M. Tang and N. Vauchelet,


Traveling wave solution of the Hele-Shaw model of tumor growth with nutrient with M. Tang and N. Vauchelet, M3AS. 2014


Beyond blow-up in excitatory integrate and fire neuronal networks: refractory period and spontaneous activity with M. J. Caceres,

Journal of Theoretical Biology 350 (2014) 81–89.


Bernoulli variational problem and beyond with A. Lorz and P. Markowich, ARMA


Long-term analysis of phenotypically structured models with A. Lorz, Proc. of the Royal Society London. Series A.


Scalar conservation laws with rough (stochastic) fluxes with P.-L. Lions and P. E. Souganidis. Stoch. PDES : anal. and comput. Vol. 1 (4), 2013, 664-686.


Effects of space structure and combination therapies on phenotypic heterogeneity and drug resistance in solid tumors with A. Lorz, T. Lorenzi, J. Clairambault and A. Escargueil.


On a voltage-conductance kinetic system for integrate and fire neural networks with D. Salort, KRM 6(4) (2013) pp. 841-864


Time fluctuations in a population model of adaptive dynamics with S. Mirrahimi and P. E. Souganidis. Ann. I. H. P. Anal. nonlinéaire


The Hele-Shaw asymptotics for mechanical models of tumor growth with F. Quiros and J.-L. Vazquez, ARMA, Vol. 212 (1), (2014) 93--127


Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies  with J. Clairambault, M. Hochberg, A. Lorz and T. Lorenzi. ESAIM:M2AN 47(2) 377-399 (2013)


Invasion fronts with variable motility      with many collaborators. CRAS (2012)


Nonlinear stability of a Vlasov equation for  plasmas  with F. Charles, B. Després and R. Sentis. KRM Vol. 6, No. 2 (2013) 269-290


Stochastic averaging lemmas for kinetic equations  with P.-L. Lions and P. E. Souganidis. Seminaire X-EDP 2012


Optimal regularizing effect for scalar conservations laws      with F. Golse (Rev. Mat. Iberoam., to appear)


Direct competition results from strong competiton for limited resource     with S. Mirrahimi, J. Wakano.  J. Math. Biol. To appear.


Relaxation and self-sustained oscillations in the time elapsed neuron network model     with  K. Pakdaman and D. Salort. SIAM J. Appl. Math.  73(3) (2013), pp. 1260-1279.


A singular Hamilton-Jacobi equation modeling the tail problem with G. Barles, S. Mirrahimi and P. E. souganidis, SIAM J. Math. Anal.  44(6) (2012) pp 4297-4319.


Analysis of a simplified model of the urine concentration mechanism  with A. Edwards, N. Seguin, M. Tournus, Netw. Heterog. Media 7(4) (2012) pp. 989-1018 (2012)


Regularization in Keller-Segel type systems...etc         with A. Vasseur Comm. Math. Sc. Vol; 10(2) (2012) 463--476.


A structured model for cell differentiation  with M. Doumic, Anna Marciniak-Czochra and J. Zubelli. SIAM J. Appl. Math. Vol. 71, No. 6, pp. 1918–1940 (2011)


Evolution of species trait through resource competition   with S. Mirrahimi, J. Wakano, J. Math. Biology, Vol. 64, No 7, pp. 1189-1223 (2012).


Model for Chronic Myelogenous Leukemia  with M. Doumic-Jauffret and P. Kim, Vol. 72(7), 1732—1759 (2010).


Can a traveling wave connect two unstable states?      with G. Nadin and M. Tang. C. R.A.S. Paris, Série I (2011).


Analysis of Nonlinear Noisy Integrate and Fire Neuron Models: blow-up and steady states  with M. J. Caceres, J. A. Carrillo. J. Math. Neurosciences 2011


Traveling plateaus for a HKS...: existence and branching instabilities      with C. Schmeiser, M. Tang, N. Vauchelet. Nonlinearity 24 (2011) 1253-1270.


Branching instabilities in Hyperbolic Keller-Segel system   with F. Cerretti, C. Schmeiser, M. Tang, N. Vauchelet.  M3AS Vol. 21, Suppl. (2011) 825--842.


Dirac mass dynamics in multidimensional nonlocal parabolic equations     with A. Lorz, S. Mirrahimi. CPDE Vol. 36(6), 2011, 1071--1098.


Mathematical description of bacterial traveling pulses     with J. Saragosti, V. Calvez, N. Bournaveas  A. Buguin and P. Silberzan  (Plos Comp. Biology, 2010)


Flashing rachets  with P. E. Souganidis. NoDEA  vol. 18(1), 45--58 (2011).


Dynamics of a structured neuron population        with  K. Pakdaman and D. Salort. Nonlinearity 23 (2010) 55--75.


Survival threshold in adaptive evolution     with M. Gauduchon. Math. Med. Biol. 27 (2010), no. 3, 195–210.

Models of self-organizing bacterial communities...   see Mathematical Modelling of Natural Phenomena Vol. 5 No 1 (2010), 148—162.

See also  arXiv (mathematics) or   archives ouvertes HAL    and    talk