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X-WR-CALDESC:Centro de Modelamiento Matemático
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DTSTART:20260812T004002
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DTSTART;TZID=America/Santiago:20260805T161500
DTEND;TZID=America/Santiago:20260805T173000
DTSTAMP:20260805T111543Z
CREATED:20260805
LAST-MODIFIED:20260805
PRIORITY:5
SEQUENCE:1
TRANSP:OPAQUE
SUMMARY:Chilean Probability Seminar: “Stochastic particle system approximation of the Keller-Segel PDE and suppression of blow-up”
DESCRIPTION:Abstract: In this talk, we will first present a system of moderately interacting stochastic particle system (singular, attractive interaction potential) whose empirical measure converges to the solution of the Keller-Segel PDE, which is a PDE known for exhibiting finite-time blow-up. In a second part, we then introduce a birth-and-death mechanism for each particle, involving a death rate proportional to the local concentration of particles. We will show that the empirical measure of this new system converges to a Keller-Segel equation with a logistic term (of KPP- type), for which explosion in finite time can be avoided.\nTime permitting, we may finally consider the collisions of the particle system with birth-and- death mechanism and non-mollified kernel, and show that as the number of particles goes to infinity, the probability of critical collisions between particles vanishes, leading to convergence\nof the empirical measure along subsequences.\nBased on joint works with T.Cavallazzi (CentraleSupélec), C.Olivera (Unicamp), S.Popat (Polytechnique), Y.Tardy (Polytechnique) and M.Tomasevic (Polytechnique).\nJoin the seminar via Zoom: https://reuna.zoom.us/j/84521834914?pwd=OTZ6Y0NWM3pYTGtTbEt3c0luTG96UT09\n
URL:https://www.cmm.uchile.cl/events/chilean-probability-seminar-stochastic-particle-system-approximation-of-the-keller-segel-pde-and-suppression-of-blow-up/
ORGANIZER;CN=CMM:MAILTO:
CATEGORIES:Seminarios
LOCATION:Sala Maryam Mirzakhani - 6to piso CMM
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