Lower Bounds of Finite-Time Blow-Up of Solutions to a Two-Species Keller-Segel Chemotaxis Model

摘要

In this paper, we investigate the blow-up phenomena of non-negative solutions of a two-species Keller-Segel chemotaxis model with Lotka-Volterra competitive source terms. We estimate the lower bounds for the blow-up time of solutions of the model under the Neumann boundary conditions in a bounded domain Ω {is truely contained in} R~n, n ≥ 1. The first-order differential inequality technique is applied to determine the results in various space dimensions by using different auxiliary functions.