Analysis Of The Properties Of The Solutions Of Higher Dimensional Degenerate Keller-Segel Equations

This paper mainly studies the properties of the solutions of the multi-species and multi-chemicals Keller-Segel chemotaxis model with degenerate effect from biomathematics.This type of model can be used to describe the collective movement behavior of populations or microorganisms.So it has a wide range of applications in ecology and life sciences.The study for the existence,uniqueness and asymptotic behavior of the solutions of such models plays a vital role on guiding experiments and practice.This thesis focuses on proving the existence and non-existence of solutions for three types multi-species and multi-chemicals Keller-Segel models by classifying the indexes and coefficients of nonlinear terms in the model.In Chapter 3,for a class of degenerate attraction-repulsion Keller-Segel equations with a species and two-chemicals in highdimensional space,the existence and blow-up behavior of the model solutions are given by classifying the exponents and parameters in detail.Specifically,in the subcritical case,the global existence of the solutions is proved;In the supercritical case,the existence and nonexistence of solutions are investigated for different situations where the repulsive potential dominates and the attractive potential dominates.Chapter 4 investigates the properties of solutions to a degenerate Keller-Segel equations with two-species and one chemical driven by the logarithmic potential in high-dimensional space.Due to the degenerate diffusion effect is stronger than the concentration effect caused by logarithmic potential,it can prove that the model has a global weak solution for any initial value.In Chapter 5,for a class of degenerate Keller-Segel equations with two-species and twochemicals driven by the Bessel potential in high-dimensional space,the global existence of solutions is given in the subcritical case.In the supercritical case,the existence and blow-up of the solution depend on the initial conditions.We obtain a critical curve which can distinguishes the existence and non-existence of the solution in the supercritical case.