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-   -   MultiDimensional Partial Differential Equations. (http://www.cfd-online.com/Forums/main/10170-multidimensional-partial-differential-equations.html)

Aditya October 28, 2005 00:51

MultiDimensional Partial Differential Equations.
 
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

Praveen. C October 28, 2005 01:22

Re: MultiDimensional Partial Differential Equation
 
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.

Tom October 28, 2005 05:03

Re: MultiDimensional Partial Differential Equation
 
Try looking in Courant and Hilbert (volume 2) or "Partial differential equations" by Garabedian.


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