My main problem to solve is anisotropic wood (2D) with tree rings paralel and all in one direction.
I'm having problem solving the equation
$$au_{xx} + bu_{yy} = -c.$$
It's a non time dependent part of temperature profile in 2D. I've already used seperation to solve that.
$$T(x,y,t) = u(x,y)\exp{(-wt)}$$
I'm trying to solve non-stationary anisotropic heat equation. The first equation above is already rotated in eigensystem of my material.
My real question is: Is this by any chance analiticaly solveable (probably not)? If not, is it possible to get the equation in shape to solve it numericaly?
I was already trying with Wolfram Mathematica 8.0 but can't get the boundary conditions to programs liking.
Bostjan
a,b,c > 0 are positive constanst
My original equation is heat equation:
a1*Txx + a2*Txy + a3*Tyy = a4*Tt
a1,a2,a3,a4 > 0 are positive constants, x,y, are coordinates, t is time
indexes are representing partial derivation by the variable.
To get to the upper eqution I had the use seperation T(x,y,t) = U(x,y)*w(t). After that I had to rotate the system in to eigensystem.
