Qualitative Analysis Of Global Boundedness To Some Chemotaxis Models

Since Keller-Segel model was proposed in 1980s,much attention has been paid on this model,especially on the qualitative analysis of the global boundedness of its solutions.Along with the development of microbiology,varieties of chemotaxis models with the significant reality contexts have been introduced in succession.As an important step to the further study of the dynamic behaviors of these models,investigations on global boundedness of the relevant initial-boundary problems have greatly theoretical and practical significance.This thesis is concerned with the global boundedness of solutions to some chemo-taxis models.The main contents are divided into four chapters.In chapter 1,we recapitulate the background of the related issues and summarize the main results of this thesis.In chapter 2,we consider the global boundedness in a quasilinear Keller Segel model with logistic source,and show the influences of the interaction between logistic source and volume filling on global solvability of this model.In chapter 3,we prove the global boundedness of the solutions to a quasilinear chemotaxis-haptotaxis model which describes the tumor cells invasion,and study the roles played by the bi-ological dynamics mechanisms therein on global solvability of the model.In chapter 4,we devote to proving the global solvability of Keller-Segel-fluid dynamics models.More precisely,for the three-dimensional degenerate Keller-Segel-Stokes model we in-vestigate the effects of the reciprocity among logistic source,porous medium diffusion and tensor-valued chemotactic sensitivity on global solvability,while for spatial dimen-sion N = 2,3,we investigate the impact of signal-dependent chemotactic sensitivity on global solvability of the Keller-Segel-(Navier-)Stokes model under consideration.