# Second-order PDE with seven variables

I need to solve the following partial differential equation in seven variables with four boundary conditions. I don't think Mathematica has the capacity to solve this differential equation.

Do you know of scientific packages which can be used to solve this equation and plot graphs of the dependent variable against each of the independent variables?

• It looks like you missed to include the actual equation. – Wrzlprmft Nov 29 '17 at 20:59
• I've attached it now. – nightmarish Nov 29 '17 at 23:00
• This equation seem to be off second order to me – nicoguaro Nov 30 '17 at 3:51
• This looks like it's only an equation in three variables ($t_x,r_x,\theta_x$) plus a time-like variable $u$. $t_y,r_y,\theta_y$ only seem to be parameters, but there are no derivatives with regards to these variables. Is this correct? If so, you basically have a 3+1 dimensional advection diffusion equation with some wacky weights. – Wolfgang Bangerth Nov 30 '17 at 6:46
• That's true. $t_y$, $r_y$ and $\theta_y$ only appear in one of the boundary conditions. How would you solve a $3+1$-dimensional advection diffusion equation with wacky weights though? – nightmarish Nov 30 '17 at 7:08