Given an initial (x)-velocity distribution of: [ u(x, 0)= begin{cases}1 & x leq 0.5 2 x

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Given an initial \(x\)-velocity distribution of:

\[ u(x, 0)= \begin{cases}1 & x \leq 0.5 \\ 2 x & 0.5

Does a shock form when the inviscid Burgers' equation is applied to this initial velocity field? Why or why not? Plot the characteristic curves.

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