Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion (Q1433449)

This paper is a continuation of [Discrete Contin. Dyn. Syst. 9, No. 5, 1193--1200 (2003; Zbl 1029.35116)] by the same authors to study the problem of global existence of strong solutions for the Shigesada-Kawasaki-Teramoto model. It is proved global existence of strong solutions assuming that there are self- and cross-diffusions in the first species and there is no cross-diffusion in the second species. It is also shown that if the self-diffusion presents in the second species then the space dimension must be less than 6.