Properties Of Solutions To Some Chemotaxis Models

A characteristics feature of living systems is that they sense the environment in which they are living and respond to the sensation. The response involves movement toward or away from an external stimulus, such a response is called a taxis. Because of the different stimulus substances, taxis are divided into different types, such as phototaxis, aerotaxis, geotaxis, chemotaxis, haptstaxis and so on. Because of that chemotaxis exists extensively and variety, more and more experts and scholars pay close attention to this phenomenon.Mathematical chemotaxis model(e.g., Keller-Segel model[1];Othmer-Stevens model[18];Levine-Sleeman model[19]), being strongly coupling nonlinear system of partial differential equation, is an interesting mathematical problem.In this thesis, the following problems are studied:●behavior of the solutions to some Othmer-stevens chemotaxis model with reproduction term;●global existence and blow-up of solutions to a parabolic-parabolic system of chemotaxis model;●global attractor existence to some chemotaxis model.In Chapter 1, we introduce briefly the background of chemotaxis model. We recall the history of mathematical research on chemotaxis and the preliminary knowledge which will be needed in this paper.In Chapter 2 and 3, we consider some Othmer-stevens chemotaxis model with reproduction term in a bounded domain: and the following multi-group chemotaxis model:By making use of function transformation, iteration and comparative method, more interesting results are arrived at.In Chapter 4, a parabolic-parabolic system of chemotaxis model is concerned: we prove the local and global existence by use of the standard estimates and semigroup theory.In Chapter 5, we discuss two parabolic-parabolic system of chemotaxis model and we proved the existence of global attractor to these models.