Consider a function U(x,y) where x, and y are spatial variables (have units of length)(adsbygoogle = window.adsbygoogle || []).push({});

Assume that the symbol V^2 corresponds to the Laplacian operator.

Then V^2U= Uxx + Uyy where the subscript indicates partial differentiation.

Consider now a function F(x,t) where x is spatial variable (has units of length) and t is a temporal variable (has units of time)

I found quite surprising that the action of the Laplacian on this new function is a little bit different than previously.

V^2F= Fxx

Could you please give me a hint as to why does this happen? Why

V^2F= Fxx + Ftt is incorrect?

What springs to mind is that Ftt has units of acceleration and Fxx represents the concavity of F parallel to XX’ axis. So we cannot really add these two different quantities. Apart from this (which I am not if it is mathematically correct) do you have any other explanation?

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# Action of Laplacian Operator

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