Boundedness Of Solutions To A Chemotaxis Model With Chemical Signaling Loop

Partial differential equations play an important role in physics,chemistry,biology,and other fields.Many experts and scholars use the strict theory of partial differential equations to study the related problems in biology.For example,the classical Keller-Segel model,which is called the chemotaxis model,it explains the directional movement of cells and microorganism under the influence of a chemical signal.Chemotaxis can be used to describe some phenomena such as bacterial aggregation,embryonic growth,tumor invasion,immune response and wounding healing.The corresponding problems can be analyzed qualitatively through the mathematical method of theoretical research.This thesis deals with the Neumann initial boundary value problem of a chemotaxis model with chemical signaling loop,and obtain the global existence and boundedness of the solutions of this model under suitable assumptions.The thesis mainly consists of the following four chapters.In Chapter one,we mainly describe the actual background and development status and a brief introduction of the main work of the chemotaxis model with chemical signaling loop.In Chapter two,some preparatory knowledge.It mainly reviews some common inequalities and the comparison principle of parabolic operators in partial differential equations,which will be used in later chapters.In Chapter three,studying the global existence and boundedness of solutions of this model.Based on the theory of heat semigroup,comparison principle of parabolic operators,construction of supersolution,Moser iteration,G-N inequality and other techniques,the global existence and boundedness of solutions to the model are obtained in the two dimensional unit disk under certain conditions of parameters.In Chapter four,summarizing the content of this thesis and put forward some prospects for the future work.