Behavior of the Solutions to an Othmer-Stevens Chemotaxis Model with Reproduction Term

In this paper, we study a simplified Othmer-Stevens model with reproduction term. By making use of a smart function transformation, the comparative method and some special mathematical analysis, we prove the existence of global, blow-up or quenching solutions of the problem on different conditions. More interesting results are reached. The result of the paper not only verifies a real biological phenomenon, but also provides a theoretical groundwork for numerical problems of the chemotaxis model.