A NOTE ON CRITICAL POINT AND BLOW-UP RATES FOR SINGULAR AND DEGENERATE PARABOLIC EQUATIONS

In this paper, we consider singular and degenerate parabolic equations u(t) = (x(alpha)u(x))(x) + u(m)(x(0), t)v(n)(x(0), t), v(t) = (x(beta)v(x))(x) + u(q)(x(0), t)v(p)(x(0), t), in (0, a) x (0, T), subject to null Dirichlet boundary conditions, where m,n,p,q >= 0, alpha, beta is an element of[0,2) and x(0) is an element of (0, a). The optimal classification of non-simultaneous and simultaneous blow-up solutions is determined. Additionally, we obtain blow-up rates and sets for the solutions. The singular rates for the derivation of the solutions are given.