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SUMMARY:A kinetic description of the strong interaction regime in a FitzHu
 g-Nagumo neural network. - Alain Blaustein (Université Paul Sabatier Toul
 ouse III)
DTSTART:20220517T123000Z
DTEND:20220517T131500Z
UID:TALK174437@talks.cam.ac.uk
DESCRIPTION:We consider the solution to a non-linear mean-field equation m
 odeling a FitzHug-Nagumo neural network. The non-linearity in this equatio
 n arises from the interaction between neurons. We suppose that these inter
 actions depend on the spatial location of neurons and we focus on the beha
 vior of the solution in the regime where short-range interactions are domi
 nant. The solution then converges to a Dirac mass. The aim of this talk is
  to characterize the blow-up profile: we will prove that it is Gaussian. M
 ore precisely\, we will compare several approaches:&nbsp\; we will first p
 resent a weak convergence result\, based on a analytic coupling method for
  Wasserstein distances\, then we will strengthen this result by obtaining 
 strong convergence estimates\, using relative entropy methods and we will 
 conclude by presenting a different approach\, inspired from the analysis o
 f Hamilton Jacobi equations\, which enables to obtain L infinity convergen
 ce estimates.
LOCATION:Seminar Room 2\, Newton Institute
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