  In this paper we study the 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 $t=+\infty$.
