Propagating terrace with infinite speed in cooperative systems with multiple types of diffusions

Abstract

This paper is concerned with the spatial propagation of cooperative systems with general diffusions including multiple types of nonlocal dispersal mechanisms. We show the diversity of long-term behavioral patterns exhibited by different components within these systems, under the assumption that the diffusion operator bring about infinite spreading speed in propagation dynamics. Specifically, we observe that certain components may manifest as propagating terraces with multiple steps, while others exhibit single-front profiles under specific conditions, but it is also possible for all components to display single-front profiles, depending on the selection of coefficients. Furthermore, we prove that the solutions tend to flatten as the spatial propagation has infinite speed.