Existence of a blow-up solution for a degenerate parabolic initial-boundary value problem

摘要

Here, before blow-up occurs, we establish the existence and uniqueness of a blow-up solution of a degenerate parabolic initial-boundary value problem, x~qu_1 - (x~βu_x)_x = x~q f(u) where q and β are given constants and f is a suitable function. We further give the sufficient condition to blow-up in finite time. Finally the blow-up set of a blow-up solution u is shown.