- #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 and A is not zero, the transofrmation to moving coordinates
[tex] x' = x- \frac{B}{2A} t [/tex]
[tex] t' =t [/tex]
takes L into a mutliple of the wave operator
Now the moving coordiantes looks very much like the galilean transforamtions i did in a relaitivity class a while ago.
Hyperbolic means the B^2 - 4AC > 0. But what does the transformation to moving coordiantes mean?
Also the solution to the second order PDE was solved by using
[tex] \xi = \alpha x + \beta t[/tex] and
[tex] \eta = \delta x + \gamma t [/tex]
Please give me a hint on how to connect the two together... i am quite lost!
Show that if L is hyperbolic and A is not zero, the transofrmation to moving coordinates
[tex] x' = x- \frac{B}{2A} t [/tex]
[tex] t' =t [/tex]
takes L into a mutliple of the wave operator
Now the moving coordiantes looks very much like the galilean transforamtions i did in a relaitivity class a while ago.
Hyperbolic means the B^2 - 4AC > 0. But what does the transformation to moving coordiantes mean?
Also the solution to the second order PDE was solved by using
[tex] \xi = \alpha x + \beta t[/tex] and
[tex] \eta = \delta x + \gamma t [/tex]
Please give me a hint on how to connect the two together... i am quite lost!