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Benoit
PERTHAME
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Update : February 2011 |
INRIA projet BANG
Mastere M2:
"Mathématiques appliquées aux sciences biologiques et biomédicales"
Course
Growth, reaction, movement and
diffusion from biology : 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.
Tumor growth and resistance to
chemotherapy : This is an ongoing
project in the team BANG
Renal flows : This is an ongoing project
with : A. Edwards
(CNRS-INSERM, ERL
7226 - UMRS 872), N. Seguin and M. Tournus
Some
other infos
A short-vitae Bibliography (recent papers)
Recent
preprints
Optimal
regularizing effect for scalar conservations laws with F. Golse
Direct
competition results from strong competiton for limited resource with S. Mirrahimi, J. Wakano.
Relaxation and
self-sustained oscillations in the time elapsed neuron network model with
K. Pakdaman and D. Salort.
Analysis of a simplified model of the
urine concentration mechanism
with A. Edwards, N. Seguin and M. Tournus (2011)
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 (2011), J. Math. Biology.
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