# PDE Mathematical Behavior

1. Aug 4, 2005

### Clausius2

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

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

$$u\frac{\partial u}{\partial x}+v \frac{\partial u}{\partial r}=\frac{1}{r}\frac{\partial}{\partial r}\Big(r \frac{\partial u}{\partial r}\Big)$$

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.