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2nd order PDE characteristics

  1. Jun 12, 2010 #1
    Why is the characteristic of

    (d/dx) + (d/dt) = 0 where d is small delta

    c = x - t and not c = x + t
     
  2. jcsd
  3. Jun 13, 2010 #2
    Because


    [tex](\partial_{x}+\partial_{t})f(x+t)=2f'(x+t)[/tex]

    While

    [tex](\partial_{x}+\partial_{t})f(x-t)=f'(x-t)-f'(x-t)=0[/tex]

    So you need solutions of the latter form u(x,t)=f(x-t), which means x-t=const are charcteristic lines.
     
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