- #1
stunner5000pt
- 1,461
- 2
define [tex] L = a \frac{\partial^2u}{\partial t^2} + B \frac{\partial^2 u}{\partial x \partial t} + C \frac{\partial^2u}{\partial x^2} = 0 [/tex]
show that if L is hyperbolic then and A is not zero the transofmartion to moving coordinates
[tex] x' = x - \frac{B}{2A} t [/tex]
[tex] t' = t [/tex]
tkaes L into a multiple of the wave operator
now how would igo about changing the variables in L to x' and t'?
i mean i could certainly find out
[tex] \frac{\partial x}{\partial u} [/tex] amd [tex] \frac{\partial t'}{\partial u} [/tex] and use this identity that
[tex] \frac{\partial u}{\partial x} = \frac{1}{\frac{\partial x}{\partial u}} [/tex]
but I am not sure how to proceed from there
please help
show that if L is hyperbolic then and A is not zero the transofmartion to moving coordinates
[tex] x' = x - \frac{B}{2A} t [/tex]
[tex] t' = t [/tex]
tkaes L into a multiple of the wave operator
now how would igo about changing the variables in L to x' and t'?
i mean i could certainly find out
[tex] \frac{\partial x}{\partial u} [/tex] amd [tex] \frac{\partial t'}{\partial u} [/tex] and use this identity that
[tex] \frac{\partial u}{\partial x} = \frac{1}{\frac{\partial x}{\partial u}} [/tex]
but I am not sure how to proceed from there
please help