Folks,

I am struggling to understand what is goin on in this attachment. Given that g(x)=0 and a=1 and

$\displaystyle f(x) = \left\{\begin{array}{cl}0 & x \leq -1\\ 1-x^2 & -1 \leq x \leq 1 \\ 0 & x \geq 1\\ \end{array}\right.$

For region 1:

How do we know that $\displaystyle x+t \leq -1$ and how how do we know that $\displaystyle x-t \leq -1$

Then how is u(x,t) zero in this region?

If I can understand region 1 I should infer the rest.

Thanks