Problem 2 (10 points) Let u(x, t) be the solution to the transport equation UtUx=0, x = R, t > 0 with the triangular 'pulse' initial value u(x,0) = X, -x, 2 x ≤ 0, x = (0, 1], 1<x≤ 2, x > 2. Sketch the graph of the solution u(x, 3) u(x, 4) in the x – y plane. In what direction does the triangular pulse move? Hint: Denote g(x) = u(x, 0) and write down the solution u(x, t) in terms of g. After that, sketch the graphs.

Fig: 1