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SUMMARY:Propagation front of biological populations with kinetic equations
  - Nils Caillerie\, University of Lyon 1
DTSTART:20160427T150000Z
DTEND:20160427T160000Z
UID:TALK65633@talks.cam.ac.uk
CONTACT:Josephine Evans
DESCRIPTION:Let us suppose that we are a team of biologists studying a pop
 ulation of bacteria. If we watch the population through a microscope\, we 
 will have many information on the dynamics of the population (how they mov
 e\, how they interact with each other) but if we want to study the front o
 f propagation (how the population invades its environment)\, it is more cl
 eaver to watch the Petri dish with the naked eye for a long time.\n\nFrom 
 a mathematical point of view\, the observations though the microscope are 
 modeled by a kinetic partial differential equation (PDE) with a parameter 
 epsilon (the higher epsilon\, the more we zoom in). To recover the naked e
 ye observations on a large time-scale\, we pass to the limit as epsilon go
 es to zero. The resulting equation is a useful tool to study the propagati
 on front of the bacterial population. Doing this\, we adopt the so-called 
 geometric optics approach for front propagation.\n\nIn this presentation\,
  we will show how it works on a very simple example. For this\, we will ne
 ed to make a short introduction to viscosity solutions of Hamilton-Jacobi 
 equation\, which are solutions of a PDE in a weak sense
LOCATION:MR14\, Centre for Mathematical Sciences
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