EXISTENCE OF CLASSICAL-SOLUTIONS FOR SINGULAR PARABOLIC PROBLEMS

Let Lu = u(xx) + bu(x)/x - u(t) with b a constant less than 1. Its Green's function corresponding to first boundary conditions is constructed by eigenfunction expansion. With this, a representation formula is established to obtain existence of a classical solution for the linear first initial-boundary value problem. Uniqueness of a solution follows from the strong maximum principle. Properties of Green's function and of the solution are also investigated.