Global Boundedness Of Solutions To A Multi-species Chemotaxis System With Logistic Source

In biological phenomena, chemotaxis is the property of individual organisms tending to ad-vantageous chemicals and away from harmful substances for better survival. Keller-Segel equations is an important model for chemotaxis, characterizing the development of population, It is widely used to model the spread of cancer.This dissertation is devoted to study the local existence, imiqueness, global existence and boundedness of solutions to the following chemotaxis muti-speies system with logistic source under homogeneous Neumann boundary conditions. The functions ui(i=1,…,N) denotes the population density of the species, and w=w(x, t) represents the concentration of the chemoat-tractant.χi,μi is the chemotactic sensitivity and the logistic growth coefficients, aij is the rate of competitive degradation. χi, μi and aij are all nonnegative.In this paper, we first give some preliminaries in chapter 1, In chapter 2, we establish the local existence of the solutions by the Banach fixed point theorem. We also prove the uniqueness of the local solution by the Gronwall inequality and energy method. In chapter 3 we prove the global existence and uniform boundedness of solutions. We use a weight function dependenting on the signal density to get the boundedness of solutions in the space of Lp(Ω). In order to prove the uniform boundedness of solutions in the space of L∞(Ω), we use the semigroup theory.