how to do this, can you sketch the graph with t and x

Problem 5: Let c(u) be a smooth function satisfying both c'(u) 0. Assume also that c(O) = 0. Consider the quasi-linear first-order PDE for u(x, t) given by u, + c(u)u, = 0, -co 0; u(x,0) = ee. (i). Sketch a few pictures of u versus x at fixed times to illustrate how u evolves as increases. (ii). By using the method of characteristics, derive a formula for the breaking time fj, defined as the minimum time in t O at which the solution u(x, t) becomes multi-valued in x. (iii). Calculate the breaking time t, explicitly for the special case where c(u) = u'