- #1
nixs
- 1
- 0
Hi there, could anyone help me on this particularly frustrating problem I am having... I have a linear parabolic homogeneous PDE in two variables with a boundary condition that is a piecewise function.
I can solve the pde (with a homogeneous BC) however trying to impose the actual BC makes it seem impossible. I think that using Green's functions will help - as I then have a convolution of the green's function with the BC - but I am finding it difficult to find any literature on this case, i.e. homogen pde & nonhomogen BCs.
Could anyone point me in the right direction? Below is the pde...
[tex]\frac{\partial u}{\partial t}+ a x \frac{\partial^2 u}{\partial x^2} + b \frac{\partial u}{\partial x}=0[/tex]
with BC:
[tex] u(x,T) = x-\rho \,\, \mbox{for}\,\, x>\rho[/tex]
[tex]\qquad =0 [/tex] otherwise
Thanks!
I can solve the pde (with a homogeneous BC) however trying to impose the actual BC makes it seem impossible. I think that using Green's functions will help - as I then have a convolution of the green's function with the BC - but I am finding it difficult to find any literature on this case, i.e. homogen pde & nonhomogen BCs.
Could anyone point me in the right direction? Below is the pde...
[tex]\frac{\partial u}{\partial t}+ a x \frac{\partial^2 u}{\partial x^2} + b \frac{\partial u}{\partial x}=0[/tex]
with BC:
[tex] u(x,T) = x-\rho \,\, \mbox{for}\,\, x>\rho[/tex]
[tex]\qquad =0 [/tex] otherwise
Thanks!