this question is from mathematical models by richard haberman 80.1. Assume that u = Umax(1 plomax)….

this question is from mathematical models by richard haberman
80.1. Assume that u = Umax(1 plomax). (a) Show that the time of intersection of neighboring characteristics (cor- responding to the collision of two observers moving with constant density) is 1 = Pmax 2umax dx 1 dp (b) If at t = 0, P(x, 0) = Pmax exp (**). (1) Sketch the initial density. (2) Determine the time of the first shock. (3) Where does this shock first occur?