I have the PDE:(adsbygoogle = window.adsbygoogle || []).push({});

(v_r)^2+(v_z)^2=p^2 where v=v(r,z), p=p(r,z).

I have some boundary conditions, of sorts:

p=c*r*exp(r/a)exp(z/b) for some constants a,b,c, at r=infinity and z=infinity

p=0 at f=r, where

(f_r)^2=p*r/v-v*v_r

(f_z)^2=p*r/v+v*v_r

Is it possible that one could obtain an analytic solution (with some unknown constants of course)? Or if one has to use numerical integration, what would be the best method?

Thanks in advance!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# 1st order PDE, quadratic in derivatives, two variables analytic solution?

**Physics Forums | Science Articles, Homework Help, Discussion**