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CATEGORIES:Partial Differential Equations seminar
SUMMARY:Aggregation of bacteria by chemotaxis: mathematica
l and numerical analysis - Nicolas Vauchelet (Univ
. Paris 13)
DTSTART;TZID=Europe/London:20161124T140000
DTEND;TZID=Europe/London:20161124T150000
UID:TALK69275AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/69275
DESCRIPTION:Chemotaxis is the phenomenon by which cells direct
their motion according to a chemical present in t
heir environment. In the case of positive chemotax
is\, strong aggregation may occur that create patc
h. From a mathematical point of view\, it leads to
the study of the so-called aggregation equation w
hich describes the interaction through a potential
. Such model can be derived thanks to a hyperbolic
limit of kinetic equations modeling the run-and-t
umble process of bacteria. In this case the intera
cting potential is pointy\, then solutions of aggr
egation equation may blow-up in finite time. In th
is work\, we propose to study the existence of wea
k measure solutions for such aggregation equation\
, which allows to define solutions beyond the blow
-up time. Our approach is based on the definition
of weak measure solutions for transport equation w
ith discontinuous coefficients. Then we investigat
e its numerical simulations and propose a numerica
l analysis.
LOCATION:CMS\, MR5
CONTACT:Ariane Trescases
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