Reaction-advection-diffusion competition models under lethal boundary conditions

<p style='text-indent:20px;'>In this study, we consider a Lotka–Volterra reaction–diffusion–advection model for two competing species under homogeneous Dirichlet boundary conditions, describing hostile environment at the boundary. In particular, deal with case in which one diffuses constant rate, whereas other has rate diffusion directed movement toward better habitat heterogeneous lethal By analyzing linearized eigenvalue problems from system, conclude that dispersion advection direction is not always beneficial, and survival may be determined by convexity of environment. Further, obtain coexistence steady-states to system instability conditions semi-trivial solutions uniqueness steady states, implying global asymptotic stability positive steady-state.</p>