摘要
In this paper, we investigate the global existence of nonnegative solutions of a two- species Keller-Segel model with Lotka-Volterra competitive source terms. By raising the regularity of a solution from L^1 to L^p（p〉1）, the existence and uniqueness of the classical global in time solution to this chemotaxis model is proved for any chemotactic coefficients X1, X2 〉 0 when the space dimension is one. Furthermore, it is shown that the model has a unique classical global solution in two and three space dimensions if the chemotactic coefficients X1 and X2 are small as compared to the diffusion coefficient d3 of the chemoattractant.
基金
This work is supported by the National Natural Science Foundation of China （Nos. 11361055, 11761063 and 11661051）, the Natural Science Foundation of Gansu Province （No. 1606RJZA038）, the National Statistical Scientific Research Projects （No. 2017LZ41）, and the Scientific Study Project for Gansu Province Institutes of Higher Learning （No. 2017B-41）.
