Differential Equation Problem. HELP

chanda0218
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Differential Equation Problem. HELP!

Ok I have the problem with the 2 Dimensions transient heat conduction equation.
\frac{du}{dt}= k\left(\frac{d^2u}{dx^2}+ \frac{d^2u}{dy}^2\right)
. I can solve it in the temporal space but actually I need to know how it beheave in the frequency space... any suggestions? i tried laplace combine with a separation of variable but i didnt reach to anywhere...

Thank you in advance
 
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It is generally the Fourier transform that is used to convert to "frequency space".
 


Mmmm indeed to solve that one in a time space one must use Furier Series, so how can I use the Furier transform to pass it to the frequency domain? i need to find how it beheave in term of the frequency w (omega)
Thank you though
 

Thread 'Volterra equation of the second kind'

There is the following linear Volterra equation of the second kind $$ y(x)+\int_{0}^{x} K(x-s) y(s)\,{\rm d}s = 1 $$ with kernel $$ K(x-s) = 1 - 4 \sum_{n=1}^{\infty} \dfrac{1}{\lambda_n^2} e^{-\beta \lambda_n^2 (x-s)} $$ where $y(0)=1$, $\beta>0$ and $\lambda_n$ is the $n$-th positive root of the equation $J_0(x)=0$ (here $n$ is a natural number that numbers these positive roots in the order of increasing their values), $J_0(x)$ is the Bessel function of the first kind of zero order. I...
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