Mathematical Sciences: RUI: Mathematical Problems from Combustion Theory

有了这笔奖金，主要研究人员将继续他们对反应性热爆炸模型的数学分析。特别是，他们将分析初始边值问题的解决方案，这些问题描述了密闭区域内扩散和非扩散热爆炸的演变，以确定爆炸将在何时何地发生。对于后一个问题，主要研究者将精确地描述爆炸奇点在到达爆炸时间时如何在空间和时间上演化。涉及燃烧和爆炸的自然现象提供了重要的科学和技术研究领域。与许多物理过程一样，通常有两种研究途径：理论和实验。这个奖项代表了燃烧的理论方法。在该报告中，主要研究人员将使用数学分析来确定容器中的热反应系统模型中爆炸发生的地点和时间以及热点的位置。

With this award the principal investigators will continue their mathematical analysis of models of reactive thermal explosions. In particular, they will analyze the solutions of initial-boundary value problems that describe the evolution of diffusive and nondiffusive thermal explosions in confined domains, in order to determine where and when explosions will take place. With regard to these latter questions the principal investigators will describe precisely how the blowup singularities evolve in space and time as the blowup time is reached. Natural phenomena involving burning and explosions offer important scientific and technological areas of investigation. As with many physical processes there are generally two avenues for study: the theoretical and the experimental. This award represents the theoretical approach to combustion. In it the principal investigators will use mathematical analysis to determine where and when explosions occur in models of thermally reactive systems in containers and the locations of hotspots.