PDE Help! = Characteristic Curves / Method of Characterization

  • Thread starter rexasaurus
  • Start date
  • #1
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1. Show that, if the velocity field (V) is a fixed (spatially constant) vector, then the characteristic curves will be a family of parallel-straight lines.



2. ut+V1ux+V2uy=f
f=S-[dell dotted with V]u

characteristic curves:
dX/dt=V1(X,Y) & dY/dt=V2(X,Y)


3. really looking for help on how to get started on this. any suggestions would be appreciated.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
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Since V is fixed (i.e. [itex]V_1(x,y) = C_1; V_2(x,y) = C_2[/itex], you can solve the parametric equations for the characteristic curves explicitly, and obtain X(t), and Y(t). What types of curves are these?
 

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