Update : May 2014
Université Pierre et Marie Curie
BC187 4, pl.
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’upmc.fr
Some mathematical models of tumor growth: Course
Research field : Mathematics and models from life sciences
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
Some other infos
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
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.