Semi-wave solutions of KPP-Fisher equations with free boundaries in spatially almost periodic media (Q2317080)

The main goals of this paper are to prove the existence and uniqueness of almost periodic semi-wave solutions of KPP-Fischer equations with free boundaries in spatially almost periodic media. More specifically, the author proves existence and uniqueness of almost periodic semi-wave solutions to the following diffusive KPP equation with free boundary: \[ \begin{gathered} u_t=u_{xx}+u(a(x)-u)), \ -\infty < x < h(t) \\ u(h(t),t)=0, \ h'(t)=-\mu u_x(h(t),t), \end{gathered} \] where \(\mu>0\) and \(a=a(x)\) is a positive, almost periodic function.