GLOBAL EXISTENCE OF SOLUTIONS TO AN ATTRACTION-REPULSION CHEMOTAXIS MODEL WITH GROWTH

An attraction-repulsion chemotaxis model with nonlinear chemotactic sensitivity functions and growth source is considered. The global-in-time existence and boundedness of solutions are proved under some conditions on the nonlinear sensitivity functions and growth source function. Our results improve the earlier ones for the linear sensitivity functions

Combining effects ensuring boundedness in an attraction-repulsion chemotaxis model with production and consumption

This paper is framed in a series of studies on attraction-repulsion chemotaxis models combining different effects: nonlinear diffusion and sensitivities and logistic sources, for the dynamics of the cell density, and consumption and/or production impacts, for those of the chemicals. In particular, herein we focus on the situation where the signal responsible of gathering tendencies for the particles' distribution is produced, while the opposite counterpart is consumed. In such a sense, this research complements two recent results, where the chemicals evolve according to different laws