system of non-homogeneous advection equations

Question

I would like to solve this system \begin{equation} \left\{ \begin{array}{lll} u_t+b_1 u_x=(r+l_1)u-l_1v,\\ v_t+b_2 v_x=(r+l_2)v-l_2u,\\ \end{array} \right. \end{equation}

First , I would like to try with Maple to solve

sys := [diff(u(x,t),t)+b1*diff(u(x,t),x)=(r+l1)*u(x,t)-l1*v(x,t), diff(v(x,t),t)+b2*diff(v(x,t),x)=(r+l2)*v(x,t)-l2*u(x,t)];

sol:=pdsolve(sys,[u,v]) assuming b1>b2;

The output looks like this :

I read some note about advection systems. Most of the papers I read deal with system of homogeneous advection equations. No thing seems relates to non-homogeneous system of advection equations. My questions are :

1) is there a simple way to find the close form solution $(u,v)$ of the above system ?

2) Under what conditions imposed on $b_1,b_2,r, l_1,l_2$, the system will admit an unique solution ?

Thanks.