I'm interested in solving a 2-D parabolic PDE (I'm pretty sure these can be transformed into the heat eqn) which takes the form:
Dt(u) = A(t,x)*Dxx(u) + B*(t,x,y)*Dxy(u) + C(t,y)*Dyy(u) - D*u
where u = u(t,x,y),
A,B,C are functions, D is a constant
t,x and y in [0,+Inf)
Initial condition: u(T,x,y) = max(K-x,0)
Boundary condition: u(t,h,L(t)) = 0 for some unspecified function L(t)
In general, can PDEs of this type be solved analytically, and how should I go about it?
Dt(u) = A(t,x)*Dxx(u) + B*(t,x,y)*Dxy(u) + C(t,y)*Dyy(u) - D*u
where u = u(t,x,y),
A,B,C are functions, D is a constant
t,x and y in [0,+Inf)
Initial condition: u(T,x,y) = max(K-x,0)
Boundary condition: u(t,h,L(t)) = 0 for some unspecified function L(t)
In general, can PDEs of this type be solved analytically, and how should I go about it?