# Solution to advection equation with variable coefficients

1. Jul 22, 2010

### lostidentity

Hi,

I'm trying to find analytical solution to an advection equation written in Spherical coordinates. It's spherically symmetric so I'm only interested in radial variances.

The equation is:
$$\frac{\partial{c}}{\partial{t}} + \frac{1}{r^2}\frac{\partial}{\partial{r}}(r^2uc) = 0$$

I've seen solutions to advection equation with variable coefficients written in non-conservative form using the method of characteristics. I'm wondering if I could use the same method to solve the above equation, which is written in conservative form. Note that both u and c are functions of both r and t.

Thanks.