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PDE for IVP on R for a transport equation

  1. Jul 16, 2013 #1
    Hi guys, I'm having trouble with a homework problem:

    I will have to solve for the IVP of a transport equation on R:

    the equations are:

    Ut-4Ux=t^2 for t>0, XER
    u=cosx for t=0, XER



    I've actually never seen a transportation problem like this and any help would be greatly appreciated, thank you!
     
  2. jcsd
  3. Jul 16, 2013 #2
    Have you learned about the method of characteristics? Suppose the right hand side were zero. Would you be able to solve the problem then?

    Chet
     
  4. Jul 16, 2013 #3

    haruspex

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    To eliminate the RHS, consider U = V(x, t) +T(t) where V satisfies the homogeneous equation and the same boundary condition.
     
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