It's an order 1 linear p.d.e., but the coefficients are quite complicated.
$$\begin{array}{ll}&\left(As_1^2+Bs_1s_2-(A+B+C)s_1+C\right)\frac{\partial}{\partial s_1}F(s_1,s_2,t)\\ +&\left(Ds_1s_2+Es_2^2-(D+E+F)s_2+F\right)\frac{\partial}{\partial s_2}F(s_1,s_2,t)\\ =&\frac{\partial}{\partial t}F(s_1,s_2,t)\end{array}$$
My particular boundary conditions are $F(1,1,t)=1$ and $F(s_1,s_2,0)=s_1$. I am mainly interested in finding out $F(0,0,t)$. However, I don't think I can do that without solving the whole equation. Any suggestion is welcome. Thanks in advance.
