When an explosive burns, gaseous products are formed as a result. The interaction of the burning solid and gas is not well understood. More specifically, the process of the gaseous product heating the explosive is yet to be explored in detail. The present work sets out to fill some of that gap using mathematical modelling: this aims to track the temperature profile in the explosive. The work begins by modelling single-step reactions using a simple Arrhenius model. The model is then extended to include three-step reaction. An alternative asymptotic approach is also employed. There is close agreement between results from the full reaction-diffusion problem and the asymptotic problem.

中文翻译：

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炸药燃烧的建模、计算和分析

当爆炸物燃烧时，会形成气态产物。燃烧的固体和气体的相互作用还不是很清楚。更具体地说，气体产物加热炸药的过程还有待详细探索。目前的工作着手使用数学建模来填补其中的一些空白：这旨在跟踪炸药中的温度分布。这项工作首先使用简单的 Arrhenius 模型对单步反应进行建模。然后将该模型扩展到包括三步反应。还采用了另一种渐近方法。完全反应扩散问题和渐近问题的结果非常吻合。