- #1
- 10
- 0
Hello, I would like to prove that the following partial differential equation is hyperbolic. u_{tt} (x,t)+ u_{xxxx} (x,t)= 0 with x \in \left[0 , 1\right] and x \in \left[0 , T \right ] . Can anyone help me? Thank you.
How to prove that the Euler-Bernoulli equation is hyperbolic
- MHB
- Thread starter mathematix89
- Start date
-
- Tags
- Hyperbolic
I'll let you read it for yourself. -DanI also read a very interesting definition on wikipedia but well...I'll let you read it for yourself. In summary, the following partial differential equation is hyperbolic.f
- #2
HallsofIvy
Science Advisor
Homework Helper
- 43,008
- 974
I presume that the last condition is that t, not x, is in [0, T]. Okay, what is the DEFINITION of "hyperbolic partial differential equation"?
- #3
- 10
- 0
yes indeed, t \in [0,T]
- #4
- 10
- 0
In general when the highest derivative in space and time is of order 2 it is obvious. But here we have a derivative in time of order 2 and in space of order 4.
the definition of these equations that I have in my possession is that given by Lawrence C Evans in his book entitled Partial differential Equations volume 19.
Here is a snippet that gives a definition of these equations (page 377)
- #5
- 1,952
- 983
If we had the book that would be great. If you can't type it out you can write it down on paper (neatly please!) and upload the picture.
-Dan
- #6
- 10
- 0
- #7
- 10
- 0
ok I'll try to send you the book or in the worst case I'll take screenshots
- #8
- #9
- #10
- 10
- 0
- #11
- 10
- 0
I also read a very interesting definition on wikipedia but well...