Thread: Transport Equation View Single Post

## Transport Equation

how do you use the change of variable:
$\xi$ = x - ct

on the PDE
ut + c ux = 0

where u(t,x) = v(t,x-ct) = v(t,$\xi$)

to get

vt = 0

I am trying to follow the steps of Peter J. Olver in this document http://www.math.umn.edu/~olver/pd_/lnw.pdf starting on pg 4 but get stuck here...i think i am missing an important calculus concept but cannot figure out what. He says to use the chain rule but i cannot figure out how that helps.

Any help GREATLY appreciated

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