Global and Blow-Up Solutions for a Class of Nonlinear Parabolic Equations

摘要

In this paper, the global and blow-up solutions for a class of nonlinear parabolic equations under the nonlinear Neumann boundary condition is investigated. By constructing auxiliary functions and using the maximum principle, we obtain the sufficient conditions for the existence of global and blow-up solutions with some appropriate assumptions. The upper estimate of the global solution and the upper bound for "blow-up time" are also provided.