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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

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# Characterisitics of a Parabolic PDE

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