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

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.

Re: MultiDimensional Partial Differential Equation
 

Try looking in Courant and Hilbert (volume 2) or "Partial differential equations" by Garabedian.