I need to transform an inhomogeneous dirichlet problem into a homogeneous one. For exeample the burgers equation: $$\begin{cases} \partial_t u(x,t) + u(x,t) \partial_x u(x,t)=0\\ u(0,t)=0,& \forall t\in [0,1]\\ u(x,0)=g(x),&\forall x\in [0,1] \end{cases} $$
So how can I transform this problem to something with zero boundaries?