The Analysis Of A Parabolic System Modelling Chemotaxis

The dynamics of biological models have received intensive studies, and it has been an important aspect in the field of non-linear partial differential equations. In this paper, we deal with a class of chemotaxis models, which were proposed by Othmer and Stevens [4] in one dimension case. We obtain some properties of the solutions, which help us to improve the understanding of the mechanism that causes the aggregation of myxobacteria.In Section I, we introduce the background and history about the related works for chemotaxis models.In Section 2, we consider the following systemwhere n is the unit outer normal vector on (?)Ω,Ω is a bounded domain in R~n with smooth boundary (?)Ω. We prove that the solution of the model exits globally, and if μ > 0, the solution has the following asymtotic behavior:In Section 3, we deal with theWe prove that the solution of the model exits globally for any positive initial data, and if...