A pde question that contains fourier series

[bcyalcin]

i have been trying to solve a pde problem for 3 days but i couldn't even find the answer,now i feel i m about to have a mental disease,anyone can help me ?the question is

u(x,0) = x

u(x,2) = 0

u(0,y) = 0

d u(1,y) / dx = 0
[ d^2 u / dx^2 ] + [ d^2 u / dy^2 ] = 0

i will really be appreciate if someone help me,for long time i have been working on this
p.s. i have tried for k > 0 and k < 0 but couldn't find anything,the only thing about what happens when k = 0 is we obtain linear equations like F(x) = Ax + B and G(y) = Cy + D,but i have no idea what i wil do in Fourier series with these

 

[LCKurtz]

i have been trying to solve a pde problem for 3 days but i couldn't even find the answer,now i feel i m about to have a mental disease,anyone can help me ?


the question is

u(x,0) = x

u(x,2) = 0

u(0,y) = 0

d u(1,y) / dx = 0



[ d^2 u / dx^2 ] + [ d^2 u / dy^2 ] = 0




i will really be appreciate if someone help me,for long time i have been working on this



p.s. i have tried for k > 0 and k < 0 but couldn't find anything,the only thing about what happens when k = 0 is we obtain linear equations like F(x) = Ax + B and G(y) = Cy + D,but i have no idea what i wil do in Fourier series with these

If $U(x,y) = X(x)Y(y)$ your X eigenvalue problem becomes$$
X'' - \lambda X = 0, X(0) = 0, X'(1) = 0$$If you let $\lambda = -\mu^2$, you should find nonzero eigenvalues.