Travelling waves for a class of cross-diffusion systems with small parameters (Q1903045)

This paper is concerned with the existence of the travelling wave solutions for some cross-diffusion systems with small parameters. By using singular perturbation method the existence of the travelling wave solutions with a speed \(c(\varepsilon)\varepsilon\) is proved. This result extends some previous results [see \textit{Y. Hosono} and \textit{M. Mimura}, J. Math. Kyoto Univ. 22, 435-461 (1982; Zbl 0521.92017) and \textit{Y. Hosono}, Jap. J. Appl. Math. 4, 297-359 (1987; Zbl 0655.92017)].