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PDE Mathematical Behavior

  1. Aug 4, 2005 #1

    Clausius2

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    Gold Member

    I am looking for an elegant way of demonstrating the parabolical behavior of the system:

    [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!
     
  2. jcsd
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