| This thesis focuses on the properties of two types of chemotaxis model solutions with singular sensitivity under homogeneous Neumann boundary conditions.By studying the chemotaxis model of alopecia areata with singular sensitivity,we prove the boundedness and asymptotic behavior of the solution.And by investigating the model of mountain pine beetle generated with singular sensitivity and indirect signal production,we obtain the global existence of the solution.The arrangement of this thesis is mainly divided into the following five chapters.In the first chapter,we introduce the background and current state of development of chemotaxis models and describe the main results of this thesis.In the second chapter,we consider the chemotaxis model for alopecia areata with singular sensitivity (?) where Ω(?)R2 denotes a domain with a smooth boundary (?)Ω,and the parameterχi,μi,r>0(i=1,2).Relying on the appropriate assumptions,through energy estimation,parabolic regular theory and semigroup estimation,we prove that the classical solution of the chemotaxis model exists and is consistently bounded.Based on the second chapter,in the third chapter,we discuss the asymptotic behavior of the solution.When the appropriate assumptions are met,by constructing the appropriate Lyapunov functional,we obtain that the global classical solution of the model converges to the steady state,and we calculate the convergence rate of the solution.In the fourth chapter,we deal with the chemotaxis model with singular sensitivity and indirect signal production (?) where Ω(?)Rn denotes a domain with a smooth boundary (?)Ω,and the parameter χ>0.Using energy estimation and operator semigroup,it is proved that the chemotaxis model exists a unique global classical solution.In the fifth chapter,we summarize the main findings of this research and puts forward the prospect of new projects. |
