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Is there an easy derivation of this? I don't understand page 13

http://www.math.uchicago.edu/~may/VIGRE/VIGRE2010/REUPapers/Turner.pdf

u(0, τ)=0 This problem has now become that of the flow of heat in an infinite bar. However, there is a slightly new condition in u(0, τ) = 0. This essentially says that at any time t, the temperature is 0 at x = 0.

wouldn't it be y=b where b is the barrier price? x=0 doesn't make sense when I try to visualize the problem. The barrier is on the y axis

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