Global Bounded Solutions For Keller-Segel Systems With Nonlinear Term

Chemotaxis describes oriented movement of cells along the concentration gra-dient of a chemical signal produced by the cells.Keller-Segel system is a well-known chemotaxis model,which possess both theoretical and practical significanceIn this paper,we study the global bounded solution for two Keller-Segel systems with nonlinear termsIn Chapter 1,we give an overview to Keller-Segel systems involving the study background and our main resultsIn Chapter 2,we introduce some concepts and lemmataIn Chapter 3,we consider the Keller-Segel system with nonlocal reaction and nonlinear diffusion in a smooth bounded domain Ω(?)RN(N>1),where m>1,σ≥ 1,α≥ 1,ξ>0 are real numbers.It is proved that if or then the problem possess a global classical solution which is uniformly boundedIn Chapter 4,we study the attraction-repulsion chemotaxis Keller-Segel system with nonlinear sensitivity in a smooth bounded domain Ω(?)RN(N>1),where m≥1,n≥1,γy≥1 are real numbers.It is shown that if or then there exists a unique global solution of non-negative bounded functions,which solves problem classically.