- #1
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I am looking for an elegant way of demonstrating the parabolical behavior of the system:
[tex]\frac{\partial u}{\partial<br /> x}+\frac{1}{r}\frac{\partial}{\partial r}(vr)=0[/tex]
[tex]u\frac{\partial u}{\partial x}+v \frac{\partial<br /> u}{\partial r}=\frac{1}{r}\frac{\partial}{\partial r}\Big(r<br /> \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!
[tex]\frac{\partial u}{\partial<br /> x}+\frac{1}{r}\frac{\partial}{\partial r}(vr)=0[/tex]
[tex]u\frac{\partial u}{\partial x}+v \frac{\partial<br /> u}{\partial r}=\frac{1}{r}\frac{\partial}{\partial r}\Big(r<br /> \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!