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 ?(?)RN(N>1),where m>1,?? 1,?? 1,?>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 ?(?)RN(N>1),where m?1,n?1,?y?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.