Homework Help: PDE problem

1. Aug 30, 2006

island-boy

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)

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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 $$\phi \in \mathfrak{D} (\mathbb{R}^{2})$$ (where $$\mathfrak{D}$$ means functions which are continuously differentiable with compact support)

solve for

$$\int_{\mathbb{R}}\int_{\mathbb{R}}Y(x,t) (\frac{\partial^{2}\phi}{\partial t^{2}} - \frac{\partial^{2}\phi}{\partial x^{2}}) (x,t) dx dt$$

Last edited: Aug 30, 2006