Question

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?

this question is from mathematical models by richard haberman

Answer 1

U= "uar (2-81 (wax) (9) differentiating both sides, d du="d[uwax 11-8| mar] d (1-11&max) Unwax (0 - 3s(way) du - Umar du = Umay ( all Imax IN 2t dx1) = "max de I max) Rearranging, Sman. du= dxi 2t speed = distance I dxi t time ар Umax It Smax time = 2t time for thereo obferveys. Queux (@gd.xy)