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Convergence and front position for an FKPP-type free boundary problem
Julien Berestycki, Sarah Penington, Oliver Tough
The free boundary problem\[ \begin{cases} \partial_tu=\frac{1}{2}Δu+u,\quad &t>0, \, x>L_t,\\ u(t,x)=0,\quad &t>0,\, x\le L_t,\\ \int_{L_t}^{\infty}u(t,y)dy=1,\quad &t> 0,\\ u(t,x)…
A free boundary problem arising from branching Brownian motion with selection
Julien Berestycki, Éric Brunet, James Nolen +1
We study a free boundary problem for a parabolic partial differential equation in which the solution is coupled to the moving boundary through an integral constraint. The problem a…
Global existence for a free boundary problem of Fisher-KPP type
Julien Berestycki, Eric Brunet, Sarah Penington
Motivated by the study of branching particle systems with selection, we establish global existence for the solution of the free boundary problem \[ \begin{cases} \partial_t…