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

A function u(x, t) satisfies the heat equation

[tex]K[/tex][tex]\frac{\delta^{2}u}{\delta x^{2}}[/tex] = [tex]\frac{\delta u}{\delta t}[/tex]

on the half line x [tex]\geq[/tex] 0 for t > 0, where [tex]K[/tex] is a positive constant. The initial

condition is

u(x, 0) = cxe[tex]^{\frac{-x^{2}}{4a^{2}}}[/tex]

with c and a being constants, and the boundary conditions are

u(0, t) = 0

u(x, t) [tex]\rightarrow[/tex] 0 as x [tex]\rightarrow[/tex] [tex]\infty[/tex]

Prove that the Fourier sine transform of u with respect to x is given by

[tex]\hat{u}[/tex](s,t) = [tex]\hat{u}[/tex](s, 0)e[tex]^{-Kts^{2}}[/tex]

Hence find the solution of the heat equation.

I have absolutely no idea what to do, and my books aren't helping at all. Anyone able to help me?

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# Homework Help: I need help to do a Fourier Sine Transform!

Can you offer guidance or do you also need help?

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