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CATEGORIES:Cambridge Analysts' Knowledge Exchange
SUMMARY:Propagation front of biological populations with k
inetic equations - Nils Caillerie\, University of
Lyon 1
DTSTART;TZID=Europe/London:20160427T160000
DTEND;TZID=Europe/London:20160427T170000
UID:TALK65633AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/65633
DESCRIPTION:Let us suppose that we are a team of biologists st
udying a population of bacteria. If we watch the p
opulation through a microscope\, we will have many
information on the dynamics of the population (ho
w they move\, how they interact with each other) b
ut if we want to study the front of propagation (h
ow the population invades its environment)\, it is
more cleaver to watch the Petri dish with the nak
ed eye for a long time.\n\nFrom a mathematical poi
nt of view\, the observations though the microscop
e are modeled by a kinetic partial differential eq
uation (PDE) with a parameter epsilon (the higher
epsilon\, the more we zoom in). To recover the nak
ed eye observations on a large time-scale\, we pas
s to the limit as epsilon goes to zero. The result
ing equation is a useful tool to study the propaga
tion front of the bacterial population. Doing this
\, we adopt the so-called geometric optics approac
h for front propagation.\n\nIn this presentation\,
we will show how it works on a very simple exampl
e. For this\, we will need to make a short introdu
ction to viscosity solutions of Hamilton-Jacobi eq
uation\, which are solutions of a PDE in a weak se
nse
LOCATION:MR14\, Centre for Mathematical Sciences
CONTACT:Josephine Evans
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