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SUMMARY:On a probabilistic approach to the parabolic-parabolic Keller-Sege
 l system - Milica Tomasevic (École Polytechnique)
DTSTART:20211116T153000Z
DTEND:20211116T163000Z
UID:TALK165892@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:Chemotaxis is a phenomenon by which a population of cells move
 s under the stimulation of a chemical signal present in its environment.  
 At the macroscopic level\, this phenomenon is modeled by the Keller-Segel 
 system\, the particularity of which is the fact that its solutions may blo
 w-up in finite time.  Motivated by the study of the  fully parabolic versi
 on of the Keller-Segel model using probabilistic methods\, we propose a st
 ochastic particle system with an unusual interaction: each particle intera
 cts with the past of all the others through a highly singular space-time k
 ernel.  We will show the existence and propagation of chaos for this syste
 m in the one-dimensional case.  We will discuss the numerical results in t
 he two-dimensional case and state an existence and uniqueness result for t
 he non-linear SDE in the McKean Vlasov sense under explicit conditions on 
 the model parameters in the multi-dimensional setting.\nThe talk will be b
 ased on several works among which one in collaboration with J-F. Jabir (HS
 E\, Russia) and D. Talay (Inria\, France). 
LOCATION:MR12  Centre for Mathematical Sciences
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