- #1

diraq

- 14

- 0

I have trouble when solving the following heat transport equation in half plane in frequency domain.

[tex](\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2})\theta(x,y)=i\beta\theta(x,y),-\infty<x<+\infty,y\geq 0;

\theta(|x|\rightarrow\infty,y)=\theta(x,y\rightarrow\infty)=0;

\frac{\partial}{\partial y}\theta(x,y)|_{y=0}=f(x)[/tex],

where [tex]i=\sqrt{-1}[/tex] is the unit of imaginary number, [tex]\beta[/tex] is a positive real constant, f(x) is a real function.

I tried to solve it in polar coordinate. [tex]\theta[/tex] can be expanded as the sum series of Bessel function of the second type, K. But the problem is K is divergent around the origin.

I really appreciate any help from you guys. Thanks.