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: {(h(u))(t) = del . (vertical bar del u vertical bar(p-2)del u) + f(u) in D x (0, t*), partial derivative u/partial derivative n = g(u) on partial derivative D x (0, t*), u(x, 0) = u(0)(x) >= 0 in (D) over bar. Here p > 2, the spatial region D in R-N (N >= 2) is bounded, and partial derivative 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.