Global Attraction and Boundary-Equilibrium Exclusion in a Symmetric Irreversible Reaction-Diffusion System

We classify the long-time dynamics of a three-species symmetric irreversible mass-conserving reaction–diffusion system with positive diffusion coefficients and homogeneous Neumann boundary conditions. A quadratic Lyapunov dissipation identity restricts the possible asymptotic states to four homogeneous equilibria. For initial data containing at least two species, a missing-species aggregate obeys a growth inequality that excludes convergence to every boundary equilibrium, and the global solution converges uniformly to the positive equilibrium; local stability yields eventual exponential L2 convergence. The proof uses the global classical boundedness and stability estimates from Nguyen and Tang (2026). It concerns this specified system and does not settle more general reaction-network persistence or global-regularity questions. Independent symbolic identity checks accompany the paper; external review and historical priority checking remain outstanding.