Global existence and blow-up results for p-Laplacian parabolic problems under nonlinear boundary conditions

This paper is devoted to studying the global existence and blow-up results for the following p-Laplacian parabolic problems: [Formula: see text] Here [Formula: see text] , the spatial region D in [Formula: see text] ([Formula: see text] ) is bounded, and ∂D is smooth. We set up conditions to ensure that the solution must be a global solution or blows up in some finite time. Moreover, we dedicate upper estimates of the global solution and the blow-up rate. An upper bound for the blow-up time is also specified. Our research relies mainly on constructing some auxiliary functions and using the parabolic maximum principles and the differential inequality technique.