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math.AP2026
Sharp dimension threshold for unique FKPP steady states and BBM recurrence
Luca Rossi, Oliver Tough
We consider the existence and uniqueness of positive, bounded stationary solutions of the Fisher-KPP equation with Dirichlet boundary conditions. We establish that stationary solut…
math.AP2025
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)…