On a non-autonomous reaction-convection diffusion model to study the bacteria distribution in a river.

In this paper, we propose a non-autonomous convection-reaction diffusion system (CDI) with a nonlinear reaction source function. This model refers to the quantification and the distribution of antibiotic resistant bacteria (ARB) in a river. The main contributions of this paper are: (i) the determination of the limit set of the system by applying the semigroups theory, it is shown that it is reduced to the solutions of the associated elliptic system (CDI)_e, (ii) sufficient conditions for the existence of a positive solution of (CDI)_e based on the Leray-Schauder's degree theory. Numerical simulations which support our theoretical analysis are also given. [ABSTRACT FROM AUTHOR]