I am struggeling with the following PDE:
$u_t+a(x,y)u_{xx}+b(x,y)u_{xy}+c(x,y)u_{yy}+d(x,y)u_{x}+e(x,y)u_{y}+f(x,y)u=0$ $u(T,x,y)=1,$
where $a,b,c,d,e,f$ are polynomials and the domain is the set $\{(t,x,y):t\in[0,T],x+y=1,x\geq0,y\geq0\}$.
I showed, however, that there exists a unique solution and I would like to have this solution explicitly, either via Maple/Matlab or by hand. My problem hereby is that this PDE is not in the right form for Matlab, Maple is not able to solve it (here my post in mapleprime) and I don't know how to handle this by hand.
Thanks a lot for your help.
Best regards,
utcyp