Ponente
Descripción
We propose a spatially resolved reaction–diffusion–advection extension of a thermochemical peptide–micelle reactor originally formulated as a lumped open-flow system. The model couples a seven-species chemical network to a thermal equation through Arrhenius kinetics and an exothermic thermochemical driver. In contrast with the spatially homogeneous formulation, the present PDE system incorporates advective transport, molecular diffusion, inlet–outlet exchange, and wall-mediated thermal losses, thereby preserving the open-reactor interpretation at the distributed level. After nondimensionalisation, the problem is written as an abstract evolution equation with a sectorial operator generating an analytic semigroup. The reaction map is locally Lipschitz in fractional Sobolev spaces, ensuring local well‑posedness. Positivity of all chemical species and a uniform lower bound for the temperature are proved directly, avoiding the Arrhenius singularity. An integral dissipative estimate is derived. Global existence follows under a natural $L^\infty$ bound. For the autonomous case, the existence of a compact global attractor is established, provided a bounded absorbing set exists. The results provide a rigorous functional framework for studying the long‑term dynamics of prebiotic chemical networks.