Partial differential equations — steady state of a heat equation with a source

Let $u(x,t)$ be the solution of the partial differential equation $u_t=16u_{xx}+2$, $0<x<7$, $t>0$ satisfying the conditions $u_x(0,t)=u(7,t)=0$ for $t>0$ and $u(x,0)=0$ for $0<x<7$. Then which of the following statements is true?