U.S.-Finland Cooperative Research on Dynamics and Control ofVolterra Integrodifferential Equations

该奖项支持弗吉尼亚理工大学数学系的Robert L.Wheeler和其他人与芬兰埃斯波赫尔辛基理工大学数学研究所的Stig-Olof Londen和其他人的合作。他们的研究涉及Volterra积分偏微分方程组、泛函微分方程和抽象Volterra方程的动力学，以及由这些方程控制的系统的控制和镇定问题。通过合作，将应用多种技术来研究这些问题：1)将有限维Volterra方程的技术与双曲型微分方程的技术相结合的经典分析方法：2)抽象方法，包括半群理论和非线性泛函分析的方法；3)用有限维系统逼近无限维抽象方程的半群方法和对偶方法，以及基于这种逼近的数值研究。芬兰研究人员在调和分析和为研究Volterra方程定性性质而开发的能量方法方面的专业知识，应该可以弥补美国研究人员在泛函微分方程、控制理论和其他与拟议研究主题相关的学科方面的优势。这六位合作的研究人员在这一应用数学领域的专业知识和生产力方面享有盛誉。他们中的三人之前的互动是卓有成效的。这两个研究小组之间扩大的合作有望对数学做出重大贡献。

This award supports Robert L. Wheeler and others of the Department of Mathematics, Virginia Tech, for collaboration with Stig-Olof Londen and others of the Institute of Mathematics, Helsinki University of Techology, Espoo, Finland. Their research concerns the dynamics of Volterra integro-partial differential equations, functional differential equations and abstract Volterra equations, and also control and stabilization problems for systems governed by such equations. Through collaboration, a variety of techniques will be applied to investigate these problems including: 1) classical analysis methods which combine techniques developed for finite dimensional Volterra equations with techniques for hyperbolic differential equations; 2) abstract methods including those from semigroup theory and nonlinear functional analysis; and 3) semigroup and duality methods whereby an infinite dimensional abstract equation is approximated by finite dimensional systems, and numerical studies based on such approximations. The expertise of the Finnish investigators in harmonic analysis and energy methods developed for the study of qualitative properties of Volterra equations should commplement the strengths of the U.S. investigators in functional differential equations, control theory and other subjects relevant to the proposed research topics. The six collaborating investigators have outstanding reputations for expertise and productivity in this area of applied mathematics. Previous interactions among three of them were fruitful. Significant contributions to mathematics can be expected from expanded collaboration between the two research groups.