GLOBAL AND BLOW-UP SOLUTIONS FOR THE NONLOCAL p-LAPLACIAN EVOLUTION EQUATION WITH WEIGHTED NONLINEAR NONLOCAL BOUNDARY CONDITION

摘要

In this paper, we investigate global existence and blow-up properties of nonnegative solutions to a nonlocal p-Laplacian evolution equation with weighted non-linear nonlocal boundary condition. By using the method of upper and lower solutions, we consider some effects of weight function and nonlinear exponent on the global and blow-up solutions. In addition, we show the blow-up rate estimate, blow-up profile and blow-up set for linear diffusion case.