+ ax auz - 17 5.7 Consider the Riemann problem for the following linear system of partial differential equations: auz = 0, at auz + = 0, at ax auz aui au2 +4 + 8 = 0. at ax ax ax (a) Write the system of equations in the form du/t + Adu/ax = 0. Find A, A+, and Al. (b) Write the general solution to the Riemann problem as in Equation (5.18). (c) Write the general solution for Au(0, t) in six different ways using Equations (5.21) and (5.27). In terms of this matrix notation, Equation (5.21) becomes (5.27a) Au(0) = Aul + A (ur - UL), Au(0) Aur - At(ur-UL), (5.27b) 1 1 Au(0) + |A|(ur-ul). (5.270) 2 u - () uz = ur - r3A03 - r2A02 - rivi x/t