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A free boundary problem from Brownian bees in the infinite swarm limit in R^d

PDE Seminar
April 1, 2021
1:50PM - 2:50PM
Online: Zoom info below

Date Range
Add to Calendar 2021-04-01 13:50:00 2021-04-01 14:50:00 A free boundary problem from Brownian bees in the infinite swarm limit in R^d Speaker:  James H. Nolen (Duke University) Title:  A free boundary problem from Brownian bees in the infinite swarm llimit in R^d Speaker's URL:  https://scholars.duke.edu/person/nolen Abstract:  I will explain analysis of a free boundary problem for a parabolic PDE in which the solution is coupled to the moving boundary through an integral constraint. The problem arises as the hydrodynamic limit of a stochastic interacting particle system involving branching Brownian motion with selection, the so-called Brownian bees model. At each branch event in the branching Brownian motion, a particle is removed from the system according to a fitness function, so that the total number of particles, N, is preserved. The free boundary PDE arises from the limit as N tends to infinity. In the large time limit, the PDE solution approaches a certain eigenfunction. We also prove that the so-called strong selection principle holds: the large N and large t limits commute for the particle system. This is joint work with Julien Berestycki, Éric Brunet, Sarah Penington. URL associated with Seminar:  https://research.math.osu.edu/pde/ Additional Dates &/or Times Zoom Link: https://osu.zoom.us/j/6146883919?pwd=M2hHVnFaMjVMb1pYT2FFZGdEVDIwdz09 Meeting ID: 6146883919 Password: 314159 Location Zoom ID 6146883919 / Password 314159 Online: Zoom info below Department of Mathematics math@osu.edu America/New_York public

Speaker:  James H. Nolen (Duke University)

Title:  A free boundary problem from Brownian bees in the infinite swarm llimit in R^d

Speaker's URL:  https://scholars.duke.edu/person/nolen

Abstract:  I will explain analysis of a free boundary problem for a
parabolic PDE in which the solution is coupled to the moving boundary
through an integral constraint. The problem arises as the hydrodynamic
limit of a stochastic interacting particle system involving branching
Brownian motion with selection, the so-called Brownian bees model. At
each branch event in the branching Brownian motion, a particle is
removed from the system according to a fitness function, so that the
total number of particles, N, is preserved. The free boundary PDE
arises from the limit as N tends to infinity. In the large time limit,
the PDE solution approaches a certain eigenfunction. We also prove that
the so-called strong selection principle holds: the large N and large t
limits commute for the particle system. This is joint work with Julien
Berestycki, Éric Brunet, Sarah Penington.

URL associated with Seminar:  https://research.math.osu.edu/pde/

Additional Dates &/or Times

Zoom Link: https://osu.zoom.us/j/6146883919?pwd=M2hHVnFaMjVMb1pYT2FFZGdEVDIwdz09
Meeting ID: 6146883919
Password: 314159

Location
Zoom ID 6146883919 / Password 314159

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