Asymptotic Behavior of One-Step Combustion Models with Multiple Reactants on Bounded Domains
Joel D. Avrin · SIAM Journal on Mathematical Analysis · 1993
The author considers reaction-diffusion systems on bounded domains modeling one-step reactions with Arrhenius kinetics in cases where the fuel consists of several species. The author assumes zero Neumann boundary conditions for the mass fractions and it is shown that one mass fraction decays to zero while, generally, residual amounts of the other species remain. These amounts are calculated explicitly from spatial averages of the initial conditions and it is shown that only if certain precise conditions are met will all mass fractions decay to zero. If additionally the temperature satisfies zero Neumann boundary conditions or fixed positive Dirichlet boundary conditions, then the temperature's asymptotic behavior is explicitly calculated as well.