Abstract: The celebrated Fisher-Kolmogorov-Petrovsky-Piscounof equation (FKPP) in one dimension for
h:ℝ×ℝ+→ℝ is:
∂th=∂2xh+h−h2,h(x,0)=h0(x).
This equation is a natural description of a reaction-diffusion model (Fisher 1937, Kolmogorov et al. 1937, Aronson 1978). It is also related to branching Brownian motion: for the Heaviside initial condition h0(x)=1x [is less than] 0 , h(x,t) is the probability that the rightmost particle at time t in a branching Brownian motion (BBM) is to the right of x.
One of the beauty of this equation is that for initial conditions that decrease sufficiently fast, a front develops, i.e. there exists a centring term m(t) and an asymptotic shape ω(x) such that [...]
Recording during the thematic meeting : "Random trees and maps: probabilistic and combinatorial aspects" the June 9, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
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h:ℝ×ℝ+→ℝ is:
∂th=∂2xh+h−h2,h(x,0)=h0(x).
This equation is a natural description of a reaction-diffusion model (Fisher 1937, Kolmogorov et al. 1937, Aronson 1978). It is also related to branching Brownian motion: for the Heaviside initial condition h0(x)=1x [is less than] 0 , h(x,t) is the probability that the rightmost particle at time t in a branching Brownian motion (BBM) is to the right of x.
One of the beauty of this equation is that for initial conditions that decrease sufficiently fast, a front develops, i.e. there exists a centring term m(t) and an asymptotic shape ω(x) such that [...]
Recording during the thematic meeting : "Random trees and maps: probabilistic and combinatorial aspects" the June 9, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities:
- Chapter markers and keywords to watch the parts of your choice in the video
- Videos enriched with abstracts, bibliographies, Mathematics Subject Classification
- Multi-criteria search by author, title, tags, mathematical area
Julien Berestycki: Vanishing corrections for the position of an FKPP front cnrs montpellier | |
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Science & Technology | Upload TimePublished on 29 Jun 2016 |
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