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# Heat equation scale invariance Watch

1. Can anyone help me understand this statement?

Looking for a solution to the heat equation

It shows that we can introduce similarity solutions to show that in special cases where the BC and IC are invariant under scaling invariance was can introduce

Where

Consider the equation and the BC/IC

a constant

And

as x goes to infinity.

We can use the scaling as mentioned before.

But apparently we can also use

The justification for having the factor is since, I quote, "because the heat-condution equation is linear it is invariant under the scaling "

I don't completely understand the point it's getting at, the heat-equation is surely invariant under scaling by any constant, but to multiply it by a scale factor of ? Is that obvious?

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Updated: March 25, 2013
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