CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Main CFD Forum

elliptic-PDE

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Display Modes
Old   November 3, 2003, 12:19
Default elliptic-PDE
  #1
mik
Guest
 
Posts: n/a
Is the following eq. elliptic PDE:

u_{tt} + u_{xx} = 0

t here is the time;
  Reply With Quote

Old   November 4, 2003, 10:25
Default Re: elliptic-PDE
  #2
salem
Guest
 
Posts: n/a
i think this pde is hyperbolic pde.
  Reply With Quote

Old   November 5, 2003, 05:06
Default Re: elliptic-PDE
  #3
Tom
Guest
 
Posts: n/a
with the + sign your equation is elliptic ( and so the idea that t is time is meaningless; i.e. the initial value problem is ill-posed).

u_{tt} - u_{xx} =0 on the other hand is hyperbolic and so the initial value problem is well-posed.

Tom.
  Reply With Quote

Old   November 5, 2003, 06:57
Default Re: elliptic-PDE
  #4
xiang
Guest
 
Posts: n/a
Thanks Tom; this is what I want to understand, -ve & +ve. How the cases you stated hold and at what condition one can decide is depend on the application ?

I appreciate your reply
  Reply With Quote

Old   November 5, 2003, 07:28
Default Re: elliptic-PDE
  #5
Tom
Guest
 
Posts: n/a
To understand this it's best to look at a book on pdes such as

Garabedian, P.R., Partial differential equations.

You want to look at sections on the Cauchy problem and Hadamard instability; this final topic demonstrates the ill-posedness of the initial value problem for your original equation.

Tom.
  Reply With Quote

Old   November 5, 2003, 07:59
Default Re: elliptic-PDE
  #6
xiang
Guest
 
Posts: n/a
I've looked to the book but felt like am lost;
  Reply With Quote

Old   November 5, 2003, 08:34
Default Re: elliptic-PDE
  #7
Tom
Guest
 
Posts: n/a
You should look for a more elementary introduction.

I was taught from the book "Partial differential equations" by W. E. Williams

you could also try

Applied Partial Differential Equations by Ockendon et al.

or any elementary introduction (just make sure it covers the Cauchy problem and Hadamard instability).

You may also want to look at volume 2 of Courant and Hilbert.
  Reply With Quote

Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Algorithm for coupled pde with all flux boundary conditions benk Main CFD Forum 3 December 28, 2010 06:09
Linear Iterative Solver + Elliptic PDE cfd101 Main CFD Forum 0 November 14, 2005 19:59
elliptic transformation in 3D Dinesh Godavarty Main CFD Forum 1 August 21, 2003 14:17
Type of PDE: Hyperbolic or Parabolic or Elliptic? Guo Main CFD Forum 6 January 26, 2001 11:42
Help Solving an Elliptic PDE Paul Safier CFX 0 October 12, 2000 13:31


All times are GMT -4. The time now is 14:39.