Research On The Properties Of Blow-up For Two Classes Of Nonlocal Diffusion Systems

In this paper,we mainly investigate the properties of two classes for nonlocal diffusion systems.Nonlocal diffusion systems are based on the classical diffusion equations.The classical diffusion equations,which are represented by Laplace operator,could be used to state some diffusion problems that only rely on one point in space.But actually,in our daily life,many diffusion problems are really complex,which are not only related to one point in space but also others around it.Thus,nonlocal diffusion operators(such as the convolution operator)have to be introduced for establishing nonlocal diffusion systems to deal with more diffusion problems.As we all know,these diffusion systems are differential equations,they could also be used to describe practical issues,such as to portray the population changes,migration of animals or transmission of germs and all that.Therefore,the study for the properties of nonlocal diffusion systems has research value.This article has following four chapters.In Chapter 1,we mainly introduce the actual background of the two classes nonlocal diffusion systems,the present research progresses on nonlocal diffusion systems and some related results in this field.Moreover,we also introduce the main research contents and related results of this paper.In Chapter 2,we introduce a nonlinear coupled nonlocal diffusion system,and discuss whether there exist global solutions.We first present the main conclusions of this chapter,then we will prove its Fujita curved surface by making Auxiliary function,building contradiction and using Fubini theorem or other ways.Similarly,we will achieve its secondary critical surface by making Banach space,using H?lder inequality and Young inequality or other methods.In Chapter 3,we investigate the blow-up properties for a nonlocal diffusion system with localized source.Firstly,we state the main conclusion in this chapter.Then we will prove the Fujita curve by making Auxiliary function and using Comparison principle or Fatou theorem.And finally,we will establish the secondary critical curve on the space-decay of initial value at infinity.In Chapter 4,we will summarize these nonlocal diffusion problems,conclusion what we achieved in this paper and make a corresponding prospect.