Mathematical Sciences: Volterra Integral Equations in Abstract Spaces

数学科学：抽象空间中的 Volterra 积分方程

• 批准号: 8906840
• 负责人: Ronald Grimmer
• 金额: $ 3.5万
• 依托单位: Southern Illinois University at Carbondale
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-08-15 至 1992-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8906840&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Volterra; Integral; Equations

Work to be done on this project concerns several related problems concerning Volterra integrodifferential equations in Banach spaces. Applications are planned to partial differential integral equations of the type occurring in the modeling of viscoelastic media and associated control problems. The work builds on earlier investigations and involves semigroups, cosine families and the related theory. Emphasis will be placed on finding appropriate settings and models which will yield qualitative information which can conveniently be applied. Specific problems to be analyzed include the examination of equations in Banach spaces which depend on data that incorporate all past history. The role of one of these equations representing the limiting equation for equations which do not depend on the full past history will be considered. A semigroup formulation for certain infinite history problems developed earlier will continue to receive attention. Work on symmetric hyperbolic systems will also be continued. The connecting theme in this effort is that of boundary control.

本课题涉及Banach空间中Volterra积分-微分方程解的几个相关问题。计划应用于粘弹性介质建模中出现的偏微分积分方程组和相关的控制问题。这项工作建立在早期研究的基础上，涉及到半群、余弦族和相关理论。重点将放在寻找适当的环境和模式上，这些环境和模式将产生便于应用的定性信息。要分析的具体问题包括检查Banach空间中的方程，这些方程依赖于包含所有过去历史的数据。这些方程中的一个表示不依赖于完整过去历史的方程的极限方程的作用将被考虑。早先提出的某些无限历史问题的半群公式将继续受到关注。关于对称双曲型系统的工作也将继续进行。这一努力的关联主题是边界控制。