Existence of classical solutions for degenerate semilinear parabolic problems

Let q be a nonnegative real number, and T be a positive real number. Existence of a unique classical solution is established for the following degenerate semilinear parabolic initial-boundary value problem: x(q) u(t) - u(xx) = f(u), 0 < x < 1, 0 < t less than or equal to T, u(x, 0) = u(0)(x), 0 less than or equal to x less than or equal to 1, u(0, t) = 0 = u(1, t), 0 < t less than or equal to T, where f and u(0) are given functions. In particular, its equivalent integral equation is established in terms of its Green's function. (C) 1999 Elsevier Science Inc. All rights reserved.