Hello! Can somebody help me find a solution of:

$\displaystyle u_{tt}-u_{xx}-a(u_t-u_x)=0$ on $\displaystyle \mathbb{R} \times (0, \infty)$

$\displaystyle u=g, u_t=h$ on $\displaystyle \mathbb{R}\times \{t=0\}$ with $\displaystyle a \in \mathbb{R}$

I do not really have an idea how to solve this.