CFD Online Logo CFD Online URL
Home > Forums > Main CFD Forum

MultiDimensional Partial Differential Equations.

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

LinkBack Thread Tools Display Modes
Old   October 28, 2005, 00:51
Default MultiDimensional Partial Differential Equations.
Posts: n/a
Dear ALL,

How do I find whether a multi-dimesional partial differential equation is hyperbolic,elliptic or parabolic.

There are more than one jacobians in the place. Can anyone sugggest any theory reference for the same.

I will appreciate the help.

Regards, Aditya
  Reply With Quote

Old   October 28, 2005, 01:22
Default Re: MultiDimensional Partial Differential Equation
Praveen. C
Posts: n/a
Look for the existence of wave-like solutions.

Hyperbolic: wave-like solutions exist

Parabolic: Damped wave-like solutions exist

Elliptic: No wave-like solutions

Substitute the ansatz

exp[i(k ∙ x - ω t)]

into the PDE and investigate the nature of ω. Here k and x are n-dimensional vectors and k ∙ x is the dot product.
  Reply With Quote

Old   October 28, 2005, 05:03
Default Re: MultiDimensional Partial Differential Equation
Posts: n/a
Try looking in Courant and Hilbert (volume 2) or "Partial differential equations" by Garabedian.
  Reply With Quote


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
Classification of partial differential equation tsunamiBTP Main CFD Forum 0 December 29, 2010 17:27
numerical integration of a set of ordinary partial differential equation wlt_1985 FLUENT 0 November 5, 2010 17:17
differential equations cosine CFX 1 May 31, 2010 07:22
free " ordinary differential equations solver" ztdep Main CFD Forum 2 March 21, 2006 02:58
How to solve the partial differential equaion zhou FLUENT 1 September 18, 2003 09:26

All times are GMT -4. The time now is 05:29.