Boundedness Of Solutions For Two Classes Of Biological Chemotaxis Models With Indirect Signals

In this paper,we study the boundedness of solutions for two kinds of chemotaxis models with indirect signals.In the first chapter,we introduce the biological background and derivative models of Keller-Segel systems of chemotaxis models,and then briefly introduce the main results of this paper.In the second chapter,we deal with the boundedness of solutions to the following chemotaxis model with indirect signals(?) under zero-flux boundary condition in a smooth bounded domain ?(?)Rⁿ(n?2),where ?>0 is a given parameter.We mainly use Neumann semigroup,Young's inequality,Holder inequality and L^p estimation in this chapter,and for any nonnegative initial date(u₀,v₀,w₀),and it is proved that if the chemotactic sensitivity parameter satisfies(?)the solution is globally bounded.In the third chapter,we consider the boundedness of solutions to the following nonlinear chemotaxis model with indirect signals(?)under zero-flux boundary condition in a smooth bounded domain ?(?)Rⁿ(n?2)with parameters,u>0,k>1.D(u),S(u)are assumed to satisfy D(u)?(u+1)^m and S(u)?(u+1)^q for all u?0 with q,m?R.We mainly use L^p estimation and Moser-Alikakos iteration in this chapter,and for all ?,k>1 and q?k,it is proved that for any nonnegative initial date(u₀,v₀,w₀),the solution is globally bounded.In the fourth chapter,we summarize the main contents of this paper,and the prospects of the next work.