The Global Existence Of Solution To Keller-Segel Equations With Nonlinear Aggregation

In this thesis, we consider the following Keller-Segel model with nonlinear concentration where n ≥ 3, the diffusion exponent q =4n+2or the diffusion exponent2n< q <4n+2.u(x, t) represents the density of bacteria, and c(x, t) represents the chemical substance concentration. We give the existence to this system by using the uniform estimates,compactness argument and energy method. In particular, this thesis will be separated into three parts. The ?rst one is the introduction and the key preliminary results; In the second part, for the exponent q =4n+2we prove the global existence of the weak solution under the small initial data. Finally, the global existence of the weak solution to the above model with the exponent2n< q <4n+2is given under a sharp initial condition.