# Solution of transport equation

I want to solve an equation

$\frac{\partial f(p,t)}{\partial t} + {\bf{v}} \nabla f(p,t) -\frac{1}{3} \nabla . {\bf{v}} p \frac{\partial f}{\partial p} - \frac{A}{p^2} \frac{\partial}{\partial p}(p^4 f)= 0$ where $v$ is velocity. I want to solve it for a cylinder one end is fixed and other end is expanding.

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Are $p,\in\mathbb{R}$ and $\mathbf{v}\in\mathbb{R}^2$? You probably want \cdot for the dot product. Is $v$ volume (wouldn't that then be a real-valued function of time)? –  bgins Mar 28 '12 at 17:12
yes, your assumption is right but $v$ is not volume, it is velocity. –  sknandi Mar 28 '12 at 17:32