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

boundary conditions:

u(x,0) = exp[-((x-14)^2)/4

2. Relevant equations

u_t = u_xx

x [tex]\in[/tex] R

3. The attempt at a solution

the problem says there is a way for this partial differential equation to be solved without computing any integrals. i know the general solution for the whole line is:

u(x,t) = 1 / sqrt(4kt) [tex]\int[/tex] exp[-((x-y)^2)/4kt] * PHI(y) dy

where PHI(y) is the boundary conditions.

is there some kind of substitution or trick to be used here to not have to compute any integral?

Thanks.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Heat/Diffusion Equation on the whole real line

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