Global solutions and blow-up time estimates for a class of parabolic equations under nonlinear boundary conditions

In this paper, we mainly study the global and blow-up solutions of a class of parabolic equations with nonlinear boundary conditions. With the aid of auxiliary functions and first-order differential inequality, we not only prove the existence of global solution but also dedicate an upper and a lower bound for blow-up time under some appropriate assumptions. Moreover, two examples are given to prove the correctness of the main results.