Consider the equation uux + uy = 0 with the initial condition u(x, 0) = h(x)...

Consider the equation uux + uy = 0 with the initial condition

u(x, 0) = h(x) = ⇢ 0 for x > 0

u_o for x < 0, with u_o< 0.

Show that there is a second weak solution with a shock along the line x = u_o y / 2

The solution in both mathematical and graphical presentation before and after the shock.

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Expert Solution

Colby Messinger answered 1 year ago

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