(Solving PDE's with Fourier Transforms) I'm wondering how exactly I should know where or when to input my initial conditions into a PDE that I've transformed, prompt below.

Question

mendicant_bias · Answer

$$\gamma_{xx}+\gamma_{yy}=0, \ \ \ x>0, \ y>0.$$
$$\gamma(x,y) \rightarrow 0 \ \text{as} \ \sqrt{x^2+y^2} \rightarrow \infty$$$$\gamma(0,y) =0, \  y > 0$$$$\gamma_y(x,0)=\frac{4x}{(4+x^2)^2}, \ x>0.$$

mendicant_bias · Answer

So what I'm doing is taking the Fourier Sine Treansform of both sides, but I still don't understand-how do I apply initial and boundary conditions to this problem in order to solve it?

mendicant_bias · Answer

@SithsAndGiggles  @dan815

mendicant_bias · Answer

Or better said, how do I know *when* to apply boundary conditions? I can't just insert them wherever I feel like it.

mendicant_bias · Answer

And this problem has mixed conditions, right? Two dirichlet and one neumann?

mendicant_bias · Answer

(?)

dan815 · Answer

hehe i dunno :) i gotta relearn PDE With FTs, I just crammed for my exam lol

mendicant_bias · Answer

Do you know who else I could ask about this stuff?

dan815 · Answer

Kainui knows all this stuff

dan815 · Answer

http://www.math.ubc.ca/~feldman/m267/pdeft.pdf http://dmpeli.math.mcmaster.ca/TeachProjects/Math3C03_14/home5.pdf http://dmpeli.math.mcmaster.ca/TeachProjects/Math3C03_14/homeSolution5.pdf This might help, look at my profs work for question 5 and 6, and the PDF is basic theory

mendicant_bias · Answer

@Kainui

mendicant_bias · Answer

And thanks, I'm looking over problems 5 and 6 now.

dan815 · Answer

he's sleeping you are better of sending him a PM the taggin stuff doesnt work well

mendicant_bias · Answer

@Kainui , when you have a PDE with mixed boundary conditions like this, should you apply an exponential transform? As far as I know (not sure) you (can? should?) only apply Fourier Sine Transforms when you have dirichlet conditions, and Fourier Cosine Transforms when you have neumann conditions.