(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

(a) Solve [tex]\frac{\partial u}{\partial t}=k\frac{\partial ^{2} u}{\partial x^{2}} - Gu[/tex]

where -inf < x < inf

and u(x,0) = f(x)

(b) Does your solution suggest a simplifying transformation?

2. Relevant equations

I used the fourier transform as:

F[f(x)] = F(w) = [tex] \frac{1}{2*pi} \int_{-inf}^{inf} f(x) e^{iwx} dx [/tex]

3. The attempt at a solution

I solved part a using fourier transform. Although I'm not 100% certain, I think my answer is pretty plausible. I'm happy to elaborate on how I solved this, but I didn't want to type it all out for naught, because that's not really my question. Anyway, I got:

[tex] u(x,t) = \int_{-inf}^{inf} [ \frac{1}{2*pi} \int _{-inf}^{inf} f(x) e^{iwx} dx ] e^{(-w^{2}k-G)t} e^{-iwx} dw [/tex]

I'm not sure how to answer part b. Any ideas?

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# Homework Help: PDE by Fourier Transform

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