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…