Mathematical Sciences: Mathematical Problems from CombustionTheory

在这个项目中，主要研究人员将分析微分方程系统，其解为几种类型的反应性热爆炸建模。特别是，他们将研究描述有限域中扩散和非扩散热爆演化的初边值问题解的定性性质。这项研究的目的是准确地预测爆炸发生的地点和时间，并研究随着爆炸时间的临近，溶液的行为如何。燃烧现象在我们日常生活的许多方面都很常见；想想汽车、厨房、供暖系统、火箭和导弹发动机。描述燃烧和爆炸现象的偏微分方程系统需要大量的计算机运算能力，但对控制方程的数学分析往往可以获得大量的洞察力。例如，在这个项目中，主要研究人员将试图通过明智地使用先验估计和边界函数来预测在密闭空间中爆炸发生的地点和时间。

In this project the principal investigators will analyze systems of differential equations whose solutions model several types of reactive thermal explosions. In particular, they will study the qualitative properties of solutions of initial-boundary value problems that describe the evolution of diffusive and nondiffusive thermal explosions in finite domains. The goal of this investigation is to predict precisely where and when explosions will occur and to study how the solution behaves as the blow-up time approaches. Combustion phenomena are common in many aspects of our daily lives; think of cars, kitchens, heating systems, rocket and missile engines. A large amount of computer power is brought to bear upon the systems of partial differential equations that describe combustion and explosion phenomena, but very often a great deal of insight can be obtained from a mathematical analysis of the governing equations. For example, in this project the principal investigators will attempt to predict where and when an explosion will occur in a confined space by means of a judicious use of a'priori estimates and bounding functions.