Blow-up phenomena for a nonlinear parabolic problem with p -Laplacian operator under nonlinear boundary condition

摘要

In this paper, we study the blow-up phenomena for a positive solution of a nonlinear parabolic problem with p-Laplacian operator under a nonlinear boundary condition. The sufficient conditions which ensure that the blow-up does occur at finite time are presented by constructing some appropriate auxiliary functions and using first-order differential inequality technique. Moreover, a lower bound and an upper bound for the blow-up time are derived when blow-up happens.