Boundedness Of Solutions For A Class Of The Biological Chemotaxis System With Logistic Source

In recent years,people's interest in the study of biological chemotaxis model has increased year by year,especially the research on the chemotaxis behavior of the Mountain Pain Beetle.This paper mainly describes a chemotaxis system of the aggregation and diffusion behavior of a Mountain Pain Beetle,studies a kind of biological chemotaxis system with Logistic source,and considers the bounded nature of the model solution under the influence of diffusion function,chemotaxis sensitive function and Logistic source.The main content of this article consists of five parts:The first chapter summarizes the biological background of the chemotaxis model studied,the research status of the chemotaxis model and the main research contents of this paper.The second chapter mainly introduces the basic concepts needed in this paper.The third chapter considers the model for the chemotaxis growth of the Mountain Pain Beetle with a general Logistic source:(?)in a smoothly bounded domain(?),t is positive.The energy method and Alikakos-Moser iteration are used to prove that under any sufficiently smooth initial boundary conditions,when m is large enough,the model has a unique global-in-time classical solution.The fourth chapter considers the high dimensional chemotaxis model of the Mountain Pain Beetle with special Logistic source:(?)in a smoothly bounded domain(?),where the diffusion coefficient D(u),the chemotaxis sensitivity function S(u)and the logistic source f(u)are satisfying(?),we prove that the above problem admits a unique global classical solution which is also uniformly bounded.The fifth chapter summarizes the research content of this paper.