Global and blow-up solutions for the nonlocal $p$-Laplacian evolution equation with weighted nonlinear nonlocal boundary condition

Abstract

In this paper, we investigate global existence and blow-up properties of nonnegative solutions to a nonlocal $p$-Laplacian evolution equation with weighted nonlinear 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.