# Diffusion equation with Dirichlet BC

1. Oct 6, 2012

### obnoxiousris

1. The problem statement, all variables and given/known data
Solve ut=kuxx
u(x,0)=0 (ψ(x))
u(0,t)=1
on the half line 0<x<infinity
(exercise 2, 3.1, Strauss)

2. Relevant equations

3. The attempt at a solution
There are two bits I don't get:

First, I know I have to make an odd or even extension to the whole line. But for both even and odd extensions, the formulae are:
u(x,t)=1/(√4∏kt)(∫(e-(x-y)2/4kt±e-(x+y)2/4kt)ψ(y)dy)
this means for u(x,0)=0, everything is multiplied by 0, which clearly isn't right.

Second, I don't know which extension to apply, it seems like both should work: I can either make an odd extension about the line x=1 or an even extension about the t axis, both will intercept the t axis at 1, hence satisfying the BC.

Any help would be greatly appreciated!

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