Greetings,(adsbygoogle = window.adsbygoogle || []).push({});

I want to find the characteristics of the following parabolic PDE

[itex]u_t + v u_x + w u_y + a(t, x,y,v,w, u) u_v + b(t, x,y,v,w, u) u_w - u_{vv} - u_{ww} = c(t,x,y,v,w,u)[/itex]

Where [itex]u=u(t,x,y,v,w)[/itex]

I know how to find the characteristics of a 2nd-order one-dimensional PDE. I also know how to find the Riemann invariants of a hyperbolic multidimensional PDE.

But how do I find the characteristics of a 2nd-order, nonlinear, multidimensional, parabolic PDE?

Any pointers or references are much appreciated.

Thanks

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

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!

# Characterisitics of a Parabolic PDE

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