- #1
Tohiko
- 8
- 0
Greetings,
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
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