Mathematical Sciences: The Mathematics of Thermal Explosion Phenomena

这项研究的重点是数学分析， 从反应性热爆炸的研究中产生的模型。 描述扩散方程演化的初值问题 在有限区域内的非扩散热爆炸将是 分析了 同样令人感兴趣的是， 热爆炸将发生，在封闭的位置， 将发展热点的船只，以及对 爆炸奇点是如何随着爆炸时间 正在接近。 描述这些问题的数学模型是 混合抛物-双曲型偏微分方程 行为 这些模型包括化学物质之间的相互作用 过程和诱发的气体动力学现象。 一个 如果要取得进展，就需要了解这种相互作用。 在点火爆炸，高速爆燃， 爆炸，以及火焰到爆炸的过渡。 这些 在意外爆炸研究中，主题至关重要。

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.