Complete blow-up of solutions for degenerate semilinear parabolic first initial-boundary value problems

摘要

Let q be a nonnegative real number, and tb be a positive constant. This paper studies integral solutions of the following degenerate semilinear parabolic first initial-boundary value problem:xqut-uxx=f(u),0 0 for u > 0, f(u) = o(u3) as u → ∞, and u0(x) ∈ C2+α([0, 1]) for some constant α ∈ (0, 1) is a nontrivial and nonnegative function such that u0″+f(u0)⩾0 in (0, 1), and u0(0) = 0 = u0(1). The complete blow-up of the integral solutions in the interval (0, 1) is investigated.