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MultiDimensional Partial Differential Equations. |
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October 28, 2005, 00:51 |
MultiDimensional Partial Differential Equations.
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#1 |
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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 |
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October 28, 2005, 01:22 |
Re: MultiDimensional Partial Differential Equation
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#2 |
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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. |
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October 28, 2005, 05:03 |
Re: MultiDimensional Partial Differential Equation
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#3 |
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Try looking in Courant and Hilbert (volume 2) or "Partial differential equations" by Garabedian.
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