Positive steady-state solutions of a competing reaction-diffusion system with large cross-diffusion coefficients
This paper deals with a coupled system of reaction-diffusion equations modeling the competition of two species with cross diffusion. It discusses the existence of positive steady-state solutions in relation to the intrinsic birth rates \(a_1\), \(a_2\) of the species and the cross diffusion coefficients \(\beta_{12}\), \(\beta_{21}\). The results show that positive steady-state solutions exist if \(a_1\) and \(a_2\) lie in certain range, or if \(\beta_{12}\) and \(\beta_{21}\) are sufficiently large.
scientific article; zbMATH DE number 902459