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

摘要

This paper is devoted to studying the global existence and blow-up results for the following p-Laplacian parabolic problems: {(h(u))t=∇⋅(|∇u|p−2∇u)+f(u)in D×(0,t∗),∂u∂n=g(u)on ∂D×(0,t∗),u(x,0)=u0(x)≥0in D‾. Here p  2, the spatial region D in ℝ^N (N ≥ 2) 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.