Dynamics of a parabolic-ODE competition system in heterogeneous environments

Abstract: This work is concerned with the large time behavior of the solutions of a parabolic-ODE hybrid system, modeling the competition of two populations which are identical except their movement behaviors: one species moves by random dispersal while the other does not diffuse. We show that the non-diffusing population will always drive the diffusing one to extinction in environments with sinks. In contract, the non-diffusing and diffusing populations can coexist in environments without sinks.