Weakly Nonlinear and Numerical Analyses of Dynamics in a Solid Combustion Model

This paper contains qualitative and quantitative comparisons between a weakly nonlinear analysis and direct numerical simulations of a free-boundary problem. The former involves modulating the most linearly unstable mode, taking a small perturbation of the neutrally stable value νc of a parameter ν related to the activation energy. Analogously, we perform the direct numerical computations near the marginally unstable value, namely, ν = νc − 2, where is rather small. We delineate the role of a different parameter σ (related to the Arrhenius kinetics) in the combustion dynamics when ν = νc − 2. In particular, the numerics show that varying σ produces a period-doubling scenario when lies approximately between 0.08 and 0.12. We describe the σ intervals within which complex dynamics occur for various values of and for ν fixed at νc − 2. When drops to approximately 0.06, the asymptotic and numerical solutions agree well for all physical values of σ.