I am looking for an elegant way of demonstrating the parabolical behavior of the system:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \frac{\partial u}{\partial

x}+\frac{1}{r}\frac{\partial}{\partial r}(vr)=0

[/tex]

[tex] u\frac{\partial u}{\partial x}+v \frac{\partial

u}{\partial r}=\frac{1}{r}\frac{\partial}{\partial r}\Big(r

\frac{\partial u}{\partial r}\Big)

[/tex]

Any idea?. I have read some ways of doing so by establishing a complicated matrix of coefficients, but it is only valid for linear equations.

Thanks in Advance!

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# PDE Mathematical Behavior

Can you offer guidance or do you also need help?

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