Let U = R = {x R : x > 0}, and let I = OU = {x R : x2 = x2 U 0}. + (a) Solve the semilinear PDE x u + dxu = u x2 u = g in on U r where g is a general smooth function. (b) For g(t) = t, plot/sketch/describe the maximal region in the (x1, x2) upper half-plane where the solution from part (a) is well-defined and smooth.