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PDE Help! = Characteristic Curves / Method of Characterization

  1. Oct 24, 2011 #1
    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.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 25, 2011 #2
    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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