A degenerate semilinear parabolic problem with a sink and a nonlocal source

Let Lambda < infinity, q and b be nonnegative constants, and sigma and a be positive constants. We consider the following degenerate semilinear parabolic first initial-boundary value problem, q b fa xi(qu)(tau) - u(xi xi) = -b/xi(2) u + sigma integral(a)(o) f(u(y, tau)) dy for 0 < xi < a, 0 < tau < Lambda, u(xi, 0) = u(0) (xi) for 0 <= xi <= a, u (0, tau) = 0 = u (a, tau) for 0 < tau < Lambda, where f and u(0) (x) are given nonnegative functions. Existence and uniqueness of the solution u are studied.