Asymptotic behaviour of a multiple step, multiple-reactant combustion model on bounded domains

Abstract

Under certain conditions and in certain regimes several multiple-step, multiple-reactant combustion phenomena have been successfully modelled in recent years by reduced mechanisms. In particular, Peters and Williams used the approximate scheme CH4+O2→3X, 3X + 02→2H20+C02 to model methane-air flames. Here X is a certain corngination of H and CO, and plays the role of an intermediate species. We here consider on bounded domains the reactiondiffusion equations corresponding to the Peters-Williams mechanism. For no-flux boundarv conditions on the mass fractions and either fixed Dirichlet or no-flux boundary conditions on the temperature, we show that the temperature and mass fractions always converge to (nonnegative) constant steady-states. We are largely able to explicitly compute these steady-states from the initial and boundary data, and we show that two distinct steady-state scenarios occur, depending on whether a certain parameter (explicitly computable from the initial data) is positive or nonpositive...