Differential Equation Problem. HELP

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SUMMARY

The discussion centers on solving the 2D transient heat conduction equation, specifically the equation \(\frac{du}{dt}= k\left(\frac{d^2u}{dx^2}+ \frac{d^2u}{dy^2}\right)\). The user seeks to understand the behavior of this equation in frequency space, having already attempted solutions using Laplace transforms and separation of variables without success. The consensus is that the Fourier transform is the appropriate tool for converting the equation to the frequency domain, allowing for analysis in terms of frequency (omega).

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Differential Equation Problem. HELP!

Ok I have the problem with the 2 Dimensions transient heat conduction equation.
[tex]\frac{du}{dt}= k\left(\frac{d^2u}{dx^2}+ \frac{d^2u}{dy}^2\right)[/tex]
. 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
 

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