Boundedness Of The Solutions Of Biochemotactic Model With Indirect Signal Production

In the past decades,more and more scholars have paid attention to the existence,uniqueness,blow up behavior and asymptotic behavior of the solutions of the classical Keller-Segel model,and a large number of research results have been obtained.The chemical substances in Keller-Segel model are directly produced by cells,However,there are few studies on the biological chemotaxis model with indirect signal production,which is used to describe the diffusion and aggregation behavior of mountain beetles.Therefore,this paper studies the bounded,existence and uniqueness of the solution of the biological chemotaxis model generated by indirect signal,there are five main parts:The first chapter introduces the background,development status and main contents of this paper.The second chapter introduces inequalities and lemmas needed in the process of proof.The third chapter,the global boundedness without weak solution of the chemotaxis model is proved by energy method and Moser iteration method.The fourth chapter,the existence and uniqueness of the weak solution of the chemotaxis model is proved by energy method.Firstly,the existence of the weak solution is obtained by means of convergence,and then the uniqueness of the weak solution is proved by means of energy method.The fifth chapter summarizes the content of this paper.