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PDE problem

  1. Aug 30, 2006 #1
    hello, can you guys give me a good resource(websites, etc) on how to solve this type of problem?

    The thing is, I'm not sure what methods are appropriate for solving this problem. I believe this is a PDE problem involving the Wave equation, but I don't know how to start.

    I would like to say though, I'm not really well-versed in PDEs, I'm good with ODEs and I am familiar with the basic concepts of PDE.

    Do I need to know Green's function or Fourier transforms to solve the problem below (so that I would know if I would need to study them)


    Consider the function Y defined by

    Y(x,t) = 1, if |x| <= t, Y(x,t) = 0 if |x|> t or t<= 0.

    For any [tex]\phi \in \mathfrak{D} (\mathbb{R}^{2})[/tex] (where [tex]\mathfrak{D}[/tex] means functions which are continuously differentiable with compact support)

    solve for

    [tex]\int_{\mathbb{R}}\int_{\mathbb{R}}Y(x,t) (\frac{\partial^{2}\phi}{\partial t^{2}} - \frac{\partial^{2}\phi}{\partial x^{2}}) (x,t) dx dt[/tex]
    Last edited: Aug 30, 2006
  2. jcsd
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