... time:1
Note that long times must be specified in terms of some characteristic time that depends on a diffusivity and a length. A similar comment applies to any limiting value of a physical parameter.
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...-directions.2
This is effectively a one dimensional problem in the $ x$-spatial variable.
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...:3
It is fairly easy to show that $ \ensuremath{\mbox{erf}}(z) = \frac{2}{\sqrt{\pi}}(z - \frac{z^3}{3} + \mathcal{O}(z^5))$.
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... general,4
There are some technical restrictions on the class of initial conditions are fairly easy to guess.
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... solution.5
Or the ``Son of York Trick''....
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