Flow-driven dynamics in a mussel-algae system with nonlinear boundary interactions

We investigate a reaction-diffusion-advection mussel-algae model with nonlinear boundary conditions, motivated by population dynamics in flowing aquatic environments. The system exhibits complex threshold behavior governed by energy conversion efficiency, flow velocity, and boundary-mediated losses. We establish conditions for global existence, boundedness, and characterize semi-trivial and coexistence steady states. By employing techniques compatible with the maximum principle under the structural assumption (H1) on the nonlinear boundary flux, along with super- and sub-solution methods, we rigorously analyze the persistence and extinction regimes. Our analysis reveal critical thresholds and bifurcations that determine species survival, with advection and nonlinear boundaries interacting to shape system dynamics. These findings generalize classical constant-flux models and offer a new framework for studying stability and bifurcation phenomena in reaction-advection-diffusion systems with biologically motivated boundary interactions.