On Chemotaxis Models with Cell Population Interactions

Department of Mathematics, University of Vanderbilt, Nashville, TN 37240

^* E-mail: zhian.wang@vanderbilt.edu

Abstract

This paper extends the volume filling chemotaxis model [18, 26] by taking into account the cell population interactions. The extended chemotaxis models have nonlinear diffusion and chemotactic sensitivity depending on cell population density, which is a modification of the classical Keller-Segel model in which the diffusion and chemotactic sensitivity are constants (linear). The existence and boundedness of global solutions of these models are discussed and the numerical pattern formations are shown. The further improvement is proposed in the end.