Mathematical Sciences: Mathematical Problems from CombustionTheory

在这个项目中，主要研究人员将分析 微分方程组，其解模拟多个 反应性热爆炸的类型。 特别是，他们将 研究初边值问题解的定性性质 价值问题，描述了扩散和 有限区域内的非扩散热爆炸。 的目标 这项调查是为了准确预测 爆炸将发生，并研究解决方案如何表现为 爆炸时间临近。 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 机. 大量的计算机能力被用来处理 偏微分方程组描述了 燃烧和爆炸现象，但很多时候， 可以通过对这些数据的数学分析来获得洞察力。 控制方程 例如，在这个项目中， 调查人员将试图预测爆炸发生的地点和时间 将通过明智地使用 先验估计和边界函数。

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.