摘要 I will report some recent development on a reaction-diffusion-advection system arising in river ecology.

Different to the classical diffusive case, now the linearized operator is of the non-self-adjoint type, which gives arise new

difficulty to the study of properties of both semi-trivial and co-existence steady states. We develop some new arguments

(an analytic approach) to overcome the emerging difficulties. Our theoretical results also provide some insights into the

understanding of the mechanism behind evolution of dispersal strategy.