6 Burgers' equation is a simple quasilinear equation that appears in models of gas dynamics, (a) Use the method of characteristics as described in...

Question on Partial Differential Equations.

Please show step by step. Thank you so much!

3.6 Burgers’ equation is a simple quasilinear equation that appears in models of gasdynamics, (a) Use the method of characteristics as described in Sect. 3.4 to find a formula forthe solution u (I, x) given the initial condition 0, x 5 0,u(0,x)= %, 0<x<a,1, x Z a.(b) Suppose a > b anda, x S 09u(0,x) = a(1—x)+bx, 0 < x <1,I), x >1. Show that all of the characteristics originating from x0 E [0, 1] meet at the samepoint (thus creating a shock).