Existence And Uniqueness Of The Solutions For Chemotaxis Problems

In the developing of modern science and technology, disciplinarian veracity is an important assurance for their development. The disciplinarian veracity is usually realised by establishing mathematical models. And reaction diffusion equations are common models in the description of mathematical systems, such as physical phenomena, chemical processes, ecological systems.At the present time, many scientists paid more and more attention to the reaction diffusion equations and attained many important results, especially in the field of physical phenomena, chemical processes, ecological systems and so on. lots of models of these fileds can be reduced to problems of the existence, uniqueness, stability and the properties of the solutions for the reaction diffusion equations.In biology, it is an important subject to study single cells, the movement of single cells can reflect the commen conditions of ecology and chemical around them directly. So the study of cells can give us many materials to study the environment around the cells. The movement of the single-cell amoebae towards the region of relatively higher or lower concentration of the chemical, this phenomenon is called chemotaxis. Chemotaxis is investigated in biology and chemical processes, meanwhile human have got many important results in medicine, especially in studying cancer-cell diffusion. In order to control the cancer cell diffusing, many scientists do some theory analysis, and use mathematical model to study the moving theory and condition of the system, so we can understand the complex chemotaxis system, clearly.The article consists of three sections. In the first section, we introduce chemotaxis and its history of development and study condition at present, meanwhile we introduce the study results at home and abroad. In the second section, we will prove existence and uniqueness of some chemotaxis equations with some reaction term, so the classical chemotaxis model will be studied in normal method. In the third section, we will prove existence and uniqueness of some hyperbolic-parabolic chemotaxis equations, meanwhile we will make chemotaxis model developed in a new field.