# elliptic-PDE

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

 November 3, 2003, 12:19 elliptic-PDE #1 mik Guest   Posts: n/a Is the following eq. elliptic PDE: u_{tt} + u_{xx} = 0 t here is the time;

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

 November 5, 2003, 05:06 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.

 November 5, 2003, 06:57 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

 November 5, 2003, 07:28 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.

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

 November 5, 2003, 08:34 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.

 Thread Tools Display Modes Linear Mode

 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 OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post benk Main CFD Forum 3 December 28, 2010 06:09 cfd101 Main CFD Forum 0 November 14, 2005 19:59 Dinesh Godavarty Main CFD Forum 1 August 21, 2003 14:17 Guo Main CFD Forum 6 January 26, 2001 11:42 Paul Safier CFX 0 October 12, 2000 13:31

All times are GMT -4. The time now is 01:47.