Biharmonic Operator -Fourier Transform.

Hi guys,

just wondering if someone out there could give me a hand with the following problem.

u(x,y) multiplied by a biharmonic operator =0.

The question is asking us to prove that this can be satisfied by S(x,k) = (S"(x,k)-k^2*S(x,k)) = 0 (which is straight forward enough)

but then to solve the function with respect to the boundary conditions:

u_x(0,y)=0 and u_y(0,y)=f(y) using Fourier Transforms.

I then have to solve the system using the convolution theorem.

if anyone is a bit of a whiz with this sort of thing, could you give me a hand?

id really appreciate it.

Thanks guys.

Re: Biharmonic Operator -Fourier Transform.

Re: Biharmonic Operator -Fourier Transform.

Hi mate,

Thanks for the help. I'm still unsure of a few things. (that solution did clarify

An initial problem I was facing).

First is,

Using the BC/IC: u_x(0,y)=0 and u_y(0,y)=f(y) how do I transform these conditions (more specifically the second one as it depends on y which is to be transformed) and then use that to find the constants c_i(k)?

Second, after getting that solution, solving the system via the convolution theorem. ( I obviously haven't attempted this one as I can't do the first part).

Thanks heaps!