Properties Of Solutions For A Class Of Chemotactic Models Generated By Indirect Signals

No species in nature exists independently,but has a close relationship with other species.Chemotaxis describes the directional movement of bacteria or microorganisms stimulated by chemical substances in the environment.Based on this phenomenon,Keller and Segel constructed the classic Keller Segel model in 1970.This model has been extensively studied by lots of mathematicians from various aspects.In this paper,we mainly studies the following chemotactic models in which the movement depends on the signal of chemical substances.(?) In this paper,the author mainly studies the global existence and large time behavior of the solution of the following chemotactic model in which movement depends on signal of chemical substances,where ?(?)Rn is a bounded domain with a smooth boundary,? ?R,?>0 and l>max {n+2/4,1} are all constants.This paper is arranged as follows:In chapter 1:We briefly introduce the background,development status and main re-search content of the model;In chapter 2:We studied the global existence of the solution of this model.Firstly,the local existence of the solution of this model is given,and then some prior estimates were used to calculate ?u?Lp.Finally,the global existence of the solution is obtained by using the standard Alikakos-Moser iterative method;In chapter 3:We studied the large time behavior of the solution of this system.In this section,we used several methods such as contradiction method,comparison principle of ordinary differential equations and Lyapunov function to verify the large time behavior of the chemotaxis model.In the case of ??0,the solution of this system satisfies:?u(·,t)?L?+?v(·,t)?L?+?w(·,t)?L??0.In the other case of ?>0,We constructed the Lyapunov functional and proved that the solution of this system satisfies:?u(·,t)-(?+/?)1/l-1?L?+?v(·,t)(?+/?)1/l-1?L?+?w(·,t)(?+/?)1/l-1?L??0,under the conditions of(?) where ?+=max{?,0}.