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One dimensional unsteady diffusion

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(See attached file for full problem description)

5.7 a) Consider one-dimensional unsteady diffusion in an absorbing medium. The causal fundamental solution E with pole at x = 0, t=0 satisfies

Reduce the problem to ordinary diffusion by the transformation E =

b) What would be the significance of the problem in which q^2 E is replaced by -q^2E? What about the fundamental solution?

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Solution Summary

This solution is comprised of a detailed explanation to reduce the problem to ordinary diffusion by the transformation.

Solution Preview

Please see the attached file.

Problem

Solve given E=0 t<0

Solution

1) The hint is to try

Hence

Substituting

2) Let's solve this diffusion equation by looking for a solution of the form

So f(p,r) is the 2 dimensional Fourier Transform of ...

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