Hello everyone,(adsbygoogle = window.adsbygoogle || []).push({});

I have a question that is bothering me a bit. I would be happy if you could give an idea or tell me a specific point to look at.

Lets say that we have an arbitrary function that obeys diffusion equation:

f = f(η), here η is the scaling parameter for pde which equals to x/√t

(Diffusion eq. becomes [itex]df/d\eta=-2\eta d^{2}f/d\eta^{2}[/itex] after scaling)

As I understood, diffusion eq. becomes an ode after scaling and it contains all the possible solutions for x and t pairs in η. Can we say that f(η) is invariant with respect to x and t? or in other words say ∂f/∂t=0 or not? What kind of physical information can we get just by lloking at f(η)?

Thanks in advance!

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# Scaling Problem in Diffusion Equation

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