Global Existence And Blow-up Of Solutions Of Nonlocal Diffusion Equations

In this paper, the current comparison principle is modified, and global existence andblow-up properties of the solutions to diffusion equations with nonlocal source or memoryterm and weighted nonlocal boundary condition are considered by using the method of upperand lower solution and auxiliary functions. The main contents of the thesis can be summarizedas follows:Chapter1considered p-Laplacian equation and porous medium equation with nonlocalsource term and inner absorption term subject to linear nonlocal boundary condition, andp-Laplacian equation with nonlocal source term under weighted nonlinear nonlocal boundarycondition. The sufficient conditions for global existence or nonexistence of solutions, blow-uprate estimate under some suitable conditions are obtained, and the influence of weight functionon whether determining the blowup of nonnegative solutions or not is found.Chapter2considered p-Laplacian equation and porous medium equation with memoryterm and inner absorption term subject to linear nonlocal boundary condition, and p-Laplacianequation with memory term under weighted nonlinear nonlocal boundary condition. Thesufficient conditions for global existence and blow-up of solutions, blow-up rate estimateunder some suitable conditions are obtained, and the influence of weight function on whetherdetermining the blowup of nonnegative solutions or not is found.The research of such kind of problem has great meaning for extending and improvingcurrent nonlinear methods and the nonlocal diffusion theories, and high potential applicationvalue.