Is it possible to numerically solve this PDE?

[AbDomen]

Hi all,

I'm a graduate student of engineering and have some knowledge of solving ODEs and PDEs - usually enough to do the simulations I need. However, I'm currently stumped by a PDE I found in a paper. I've attached the PDE in question (the Herring-Trilling equation) to this post.

I'm wondering - is it even possible to numerically obtain a solution for R as a function of time? The two variables are R and pL (other elements are constants), but for my purposes it'd also be okay to set pL as constant. While most of the PDE is nothing special, the first term contains the partial derivative of the time-derivative of R, in the direction of R. That has me completely baffled, and I have no idea how to even start solving it numerically.

I apologize if this is the wrong place to post my question, but I'm stumped and would be very grateful for any help. Thank you!

 

[gtoguy97]

The Herring-Trilling equation:\frac{\partial R}{\partial t} = \frac{1}{\rho_0R^2}\frac{\partial}{\partial R}\left(K\frac{\partial R}{\partial R}\right) + \frac{1}{\rho_0}\left(\frac{\partial p_L}{\partial t} - \frac{4}{3}\nu_s\frac{\partial R}{\partial t}\right)