Problem 1: 1D Burgers Equation Consider 1D Burgers Equation, with the following boundary conditions Problem 1: Problem 2: Ət + Ju d(u²/2) მ 0, u1(x, 0) = 1, u1(x, 0)=1+x, u₁(x, 0) = 2, if x < 0 if 0 ≤ x ≤1 if x > 0. u2(x, 0) = 2, if x < 0 u2(x, 0) 2x, if 0 ≤ x ≤1 u2(x, 0) = 1, if x > 1. Draw two sets of characteristics, one for each problem. Feel free to do so by hand, but include it in a pdf file. Do you observe a solution with a shock or a rarefaction wave? HINT: Take your time and double-check the solution so that you can use it to verify the correctness of your code on the next page. Upload a .pdf file with your solution below.

Fig: 1