Damped waves — an energy that decreases

Let $u(x,t)$ be the solution of the initial-boundary value problem

$$u_{tt}-u_{xx}+u_t=0, 0<x<\pi, t>0,\qquad u(0,t)=u(\pi,t)=0, t>0,$$

$$u(x,0)=\sin x, u_t(x,0)=0, 0<x<\pi .$$

For $t\ge0$, define $E(t)=\int_0^{\pi}\left(u_t^2+u_x^2\right)\mathrm{d}x$. Then which of the following statements are true?