Boundedness Of Solution For The Chemotaxis Model With Indirect Signal Absorption And Logistic Source

Over the years,many scholars and experts have been keen to study chemotaxis models in biomathematics.In particular,many results have been achieved in the study of the existence,boundedness and progressive behavior of a class of chemotactic models on indirect signal absorption.Study a kind of quasi-linear chemotactic model with indirect signal absorption:Ω（?）Rn represents a bounded domain with a smooth boundary（?）Ω,the parametersμ>0.u=u（x,t）and v=v（x,t）represent cell density and oxygen concentration,respectively,u₀,v₀,w₀ are given non-negative function,（?）/（?）u represents the directional derivative along the outer normal,and μ（u-u²）is the logistic source,represents the reproduction and growth of cells over time,and-vw represents the consumption of chemical inducers.This paper is mainly developed from the following sections:The first chapter this article first introduces the biological background of chemotactic models and the current research status of chemotactic models at home and abroad,and introduces the main content of this article.The second chapter mainly introduces some basic lemmas used in the proof process of this article.The third chapter use the energy method and semigroup theory to prove that the nonlinear diffusion coefficient D（u）and the chemotaxis sensitivity coefficient S（u）satisfy D（u）≥（u+1）m-1 and S（u）≤（u+1）q-1 in the two-dimensional situation,Under the conditions ofδ>τ,m>q-1-（?） and 1<q≤2,the solution of the chemotactic model is globally bounded,where （?）,λ₀ is Normal number.The fourth chapter use the energy method and semigroup theory to prove that the nonlinear diffusion coefficient D（u）and the chemotaxis sensitivity coefficient S（u）satisfy D（u）≥ u^m-1 and S（u）≤u^q-1 in the high-dimensional situation,δ=τ=1.Under the condition of m>max{1,2q-3},the solution of the chemotactic model is globally bounded.The fifth chapter summarizes the research content of this paper and proposes prospects.