On the multi-dimensional advective Lotka-Volterra competition systems

Reaction-advection-diffusion systems are widely used to model the population dynamics of mutually interacting species in ecology, where diffusion describes the random dispersal of species, advection accounts for the directed dispersal due to the population pressures from interspecies, and the reaction term represents the population growth of species. This paper is devoted to the studies of global-in-time solutions and nonconstant positive steady states of a class of two-species Lotka-Volterra competition systems with advection over multi-dimensional bounded domains. We prove the global existence and boundedness of positive classical solutions to the system provided that the sensitivity function decays super-linearly. The existence and stability of nonconstant positive steady states are obtained through rigorous bifurcation analysis. Moreover, numerical simulations of the emergence and evolution of spatial patterns are performed to illustrate and verify our theoretical results. These nonconstant solutions can be used to model the segregation phenomenon through inter-specific competitions.