Pointwise Estimates Of Solutions To The Cauchy Problems For Two Classes Of Keller-Segel Equations

In this thesis,we are concerned with the Cauchy problems for the Keller-Segel system with logistic source term and the Keller-Segel system with cross diffusion term.This kind of model can be used to describe the chemotaxis.With the aid of fundamental solution and Green function,we can solve the above problems and obtain the formal solutions.Then,we are able to derive the pointwise estimates for the solutions.In the meanwhile,the decay rates for the solutions are also given.For the model with logistic source term,we focus on the impact of parameters in the equation;while for the model with cross diffusion term,we have to analyze the Green function for the linearized equation and construct some proper iteration scheme,so as to prove the convergence for the iteration sequences.