Pattern Formation And Asymptotic Limits For A Chemotaxis Model With Mixed Boundary Condition

Chemotaxis is the directional movement of living organisms(such as cells or bacte-ria)stimulated by chemical signals(such as nutrients)in the surrounding environment.It describes the aggregation phenomenon of living bodies commonly seen in nature,such as the massive outbreak of bacteria and the recovery of wounds.Therefore,chemotaxis models have strong applications in the fields of microbiology,physiology and Marine ecology.In this thesis,we study the pattern formation and asymptotic behaviors of so-lutions to a chemotaxis model with logistic growth term,where the nutrient satisfies no-flux boundary condition on one boundary point and Dirichlet boundary condition on the other boundary point.We first employ the global bifurcation theory to show the existence and uniqueness of non-constant steady state to the model with some bio-logical parameters.Then using the L2 theory and Schauder theory of elliptic equations and the bootstrap argument,we establish uniform estimates for the solutions,and s-tudy the asymptotic limit as the chemotaxis coefficients tend to infinity.The results show that even if there is the capacity of the environment,the bacteria can still form a pattern which concentrates at the boundary where the nutrient enters.