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CATEGORIES:Probability
SUMMARY:On a probabilistic approach to the parabolic-parab
olic Keller-Segel system - Milica Tomasevic (Ă‰cole
Polytechnique)
DTSTART;TZID=Europe/London:20211116T153000
DTEND;TZID=Europe/London:20211116T163000
UID:TALK165892AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/165892
DESCRIPTION:Chemotaxis is a phenomenon by which a population o
f cells moves under the stimulation of a chemical
signal present in its environment. At the macrosc
opic level\, this phenomenon is modeled by the Kel
ler-Segel system\, the particularity of which is t
he fact that its solutions may blow-up in finite t
ime. Motivated by the study of the fully parabol
ic version of the Keller-Segel model using probabi
listic methods\, we propose a stochastic particle
system with an unusual interaction: each particle
interacts with the past of all the others through
a highly singular space-time kernel. We will show
the existence and propagation of chaos for this s
ystem in the one-dimensional case. We will discus
s the numerical results in the two-dimensional cas
e and state an existence and uniqueness result for
the non-linear SDE in the McKean Vlasov sense und
er explicit conditions on the model parameters in
the multi-dimensional setting.\nThe talk will be b
ased on several works among which one in collabora
tion with J-F. Jabir (HSE\, Russia) and D. Talay (
Inria\, France).
LOCATION:MR12 Centre for Mathematical Sciences
CONTACT:Perla Sousi
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