Mathematical Theories of the Thermistor Problem

热敏电阻问题的数学理论

• 批准号: 9803236
• 负责人: Xiangsheng Xu
• 金额: $ 5.42万
• 依托单位: Mississippi State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 2001-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9803236&HistoricalAwards=false
• 关键词: Mathematical; Theories; Thermistor; Problem

The principal investigator will study mathematical models that describe the combined processes of heat conduction and electrical conduction in certain semiconductors. Thermal conductivity and electrical conductivity are assumed to be highly temperature-dependent. Due to the presence of strong degeneracy and quadratic nonlinearities in the partiual differential equations that describe these processes, these physical problems lead to deep and intriguing questions in nonlinear analysis. Part of the mathematical analysis involves the applications of partial regularity and the local description of a solution near a singularity. However, solutions in these processes exhibit rich structures and different structures require different mathematical approaches.How to control temperature in microprocessors is a very important issue in the semiconductor industry. The planned research will use mathematical models to reveal how the temperature in a semiconductor depends on the known data. It is expected that the understanding of these issues can assist engineers and researchers in the design of future products.

首席研究员将研究描述某些半导体中热传导和电传导的组合过程的数学模型。 热导率和电导率被认为是高度依赖于温度的。由于描述这些过程的偏微分方程具有强退化性和二次非线性，这些物理问题在非线性分析中引起了深刻而有趣的问题。 部分数学分析涉及部分正则性的应用和奇点附近解的局部描述。 然而，这些过程中的解决方案呈现出丰富的结构，不同的结构需要不同的数学方法。如何控制温度在微处理器是一个非常重要的问题，在半导体工业。计划中的研究将使用数学模型来揭示半导体中的温度如何取决于已知数据。希望对这些问题的理解能够帮助工程师和研究人员设计未来的产品。