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First Order Nonlinear Partial Differential Equation

  1. Dec 6, 2011 #1
    I have derived a first order nonlinear PDE with its corresponding initial and boundary conditions given by:

    dv/dt + A*(v^2)*dv/dx = 0 (where A is a constant)

    v(t = 0) = C (constant value)
    v(x = 0) = 0

    I'm not quite sure how to solve this. I was thinking about using the method of characteristics, but since I haven't had too much experience with it, I'm not sure if it would be applicable here. If anyone has any hint on how to get started, I would really appreciate it. Thanks in advance.
     
  2. jcsd
  3. Dec 6, 2011 #2

    epenguin

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    I have no experience either but to get started what I would do is write that

    [tex]\frac{∂v}{∂t}/\frac{∂v}{∂x} = -Av^2[/tex]

    Then at constant v

    [tex]( \frac{dx}{dy})_v = Av^2 [/tex]

    [tex]x = Av^2t + K [/tex] at constant v.

    Fitting that to your initial conditions generates your surface I think. :uhh: Something like that.
     
  4. Dec 7, 2011 #3
    Solved! Thanks!
     
  5. Dec 7, 2011 #4

    epenguin

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    They don't count that as non-linear AFAIK though.
     
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