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CATEGORIES:Partial Differential Equations seminar
SUMMARY:An asymptotic preserving scheme for a kinetic equa
tion describing propagation phenomena - Hélène Hiv
ert (ENS Lyon)
DTSTART;TZID=Europe/London:20170213T150000
DTEND;TZID=Europe/London:20170213T160000
UID:TALK69537AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/69537
DESCRIPTION:The run-and-tumble motion of bacteria such as E. C
oli can be represented by a kinetic equation consi
dered with an hyperbolic scaling\, and a Hopf-Cole
transformation that makes the problem become non-
linear. It has been proved that the asymptotic mod
el is a Hamilton-Jacobi equation\, in which the Ha
miltonian is implicitely defined.\nStiff terms app
ear in the kinetic equation when getting close to
the asymptotic. From a numerical point of view\, i
t may make the resolution of the equation hard\, u
nless an appropriate strategy is used. Asymptotic
Preserving (AP) schemes are designed to deal with
these difficulties\, since they are stable along t
he transition from the mesoscopic to the macroscop
ic scale.\nI will present an AP scheme for this no
nlinear kinetic equation\, which is based on a for
mal asymptotic analysis of the problem\, and on a
adaptation of an AP strategy designed for a linear
kinetic equation.
LOCATION:CMS\, MR13
CONTACT:Ariane Trescases
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