Mathematical Sciences: Problems for Two Classes of Evolutionary Partial Differential Equations

数学科学：两类演化偏微分方程问题

• 批准号: 9215111
• 负责人: Hans Engler
• 金额: $ 3.25万
• 依托单位: Georgetown University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-01-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9215111&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Two; Classes

This project seeks to derive properties of solutions of two classes of partial differential equations that arise in models for the time-dependent behavior of viscoelastic model materials. The first part deals with linear integrodifferential equations that describe materials with long-term memory and their solutions. A goal is to give a detailed description of the smoothness of solutions depending on the data. The methods to be employed involve various transformation and transfer techniques that allow use of known properties of simpler, related problems. As a result, a better understanding of theoretical models and improved insight into the behavior of computational methods will is expected. Work will also be done investigating a class of nonlinear partial differential equations describing model materials with internal friction. The goal is to construct generalized solutions that obey the basic physical principle that matter cannot penetrate itself and to analyze their structure. Techniques that have been successful for other classes of nonlinear partial differential equations, such as a priori estimates, are to be employed. As a result, improved understanding of certain classes of models in continuum mechanics and more generally of solutions of partial differential equations that are to describe one-to-one mappings should result.

本项目旨在推导两个方程的解的性质 模型中出现的一类偏微分方程 粘弹性模型材料的时间依赖行为。 第一部分讨论线性积分微分方程 描述了具有长期记忆的材料及其 解决方案 一个目标是详细描述 解决方案的平滑度取决于数据。 该方法的 所采用的技术涉及各种转化和转移技术 允许使用更简单的相关问题的已知属性。 因此，更好地理解理论模型和 对计算方法行为的深入了解将 有望 工作也将做调查一类非线性 描述模型材料的偏微分方程 内部摩擦 目标是构建广义的 遵循基本物理原理的解决方案 无法穿透自身并分析其结构。 其他类别的成功技术 非线性偏微分方程，例如先验的 估计，应该使用。 因此，改善 理解连续介质力学中的某些模型类别 更一般的偏微分方程的解 描述一对一映射。