| Abstract: |
| I will talk about entire solutions of the Fisher-KPP equation $u_t=u_{xx}+f(u)$ on the half line $[0,\infty)$ with Dirichlet boundary condition at $x=0$. (1). For any $c \geq 2 \sqrt{f'(0)}$,
we show the existence of an entire solution $ \mathcal{U}^c (x,t)$ which connects the traveling wave solution $\phi^c (x+ct)$ at $t= - \infty$ and the unique positive stationary solution $V(x)$ at $t = +\infty$; (2). We also construct an entire solution $\mathcal{U} (x,t)$ which connects the solution of $\eta_t = f(\eta)$ at $t= -\infty$ and $V(x)$ at $t= +\infty$. Our result presents a rather complete description on the relationship among the entire solutions. |
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