Existence of classical solutions for degenerate semilinear parabolic problems

Abstract

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 qu t−u xx=f(u), 0<x<1, 0<t⩽T,u(x,0)=u 0(x), 0⩽x⩽1, u(0,t)=0=u(1,t), 0<t⩽T, where f and u 0 are given functions. In particular, its equivalent integral equation is established in terms of its Green's function.