3.1 Consider the conservation equation with a constant velocity c > 0, +c = 0, x at on the quadrant t 0, x 0. Suppose the boundary and initial conditions are for g, h = C[0, 00). [u(0, x) = g(x), x 0. u(t,0)=h(t), t0, (a) Find a formula for the solution u(t, x) in terms of g and h. (b) Find a matching condition for g and h that will ensure that u(t, x) is a C function.