Mathematical Sciences: The Mathematics of Thermal Explosion Phenomena

本研究的重点是对反应性热爆炸产生的模型进行数学分析。初值问题描述扩散和非扩散热爆炸在有限域的演化将进行分析。同样令人感兴趣的是准确预测何时会发生热爆炸，在密闭容器中热点将发展的位置，以及随着爆炸时间的临近，爆炸奇点如何演变的精确描述。描述这些问题的数学模型是具有混合抛物-双曲性质的偏微分方程。这些模型包括化学过程和诱导的气体动力学现象之间的相互作用。如果要在点火爆炸、高速爆燃、爆轰以及火焰向爆轰的转变等方面取得进展，就需要了解这种相互作用。这些题目对研究意外爆炸是至关重要的。

This research is focused on a mathematical analysis of models arising from the study of reactive thermal explosions. Initial value problems that describe the evolution of diffusive and nondiffusive thermal explosions in confined domains will be analyzed. Also of interest is the prediction of exactly when thermal explosions will occur, the location in the confined vessel where hotspots will develop, and a description of precisely how the blowup singularities evolve as the blowup time is approached. The mathematical models which describe these problems are partial differential equations with mixed parabolic-hyperbolic behavior. These models include the interaction between chemical processes and the the induced gasdynamic phenomena. An understanding of this interaction is needed if progress is to be made on ignition explosions, high speed deflagrations, detonations, and the transition of flames to detonations. These topics are vital in the study of accidental explosions.