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!

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

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