0, Consider the one-dimensional Euler equations ap a(pu) + at ac a(pu) a(pu² + p) + at ar де au(e + p)) + at where the p

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0, Consider the one-dimensional Euler equations ap a(pu) + at ac a(pu) a(pu² + p) + at ar де au(e + p)) + at where the pressure satisfies the ideal gas law = 0, , 0, дх 1 p=(3-1)(e-5pm) e- Suppose (p, u, e)" is close to a constant state (po, uo, eo) eo)?: P = Po +6õ, u = 10 + cũ, e = eo +6ẽ. Linearize the Euler equations for small e to find the equations for p, ū and ē. Given the initial data 1 if x < 0, 1 if x < 0, 1 if x < 0, = ū(2,0) = 0 if x > 0 -1 if x > 0 (x) = 1 if x > 0, (x,0) = { = ē(3,0) = { find the solution to the equations for po = 1, U = 0, eo = 5/2 and 7 = 7/5.