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

该奖项支持罗伯特L。惠勒和其他部门的 数学，弗吉尼亚理工大学，与Stig-Olof Londen合作 和其他数学研究所，赫尔辛基大学 芬兰，埃斯波，技术部。 他们的研究关注的是 沃尔泰拉积分-偏微分方程，泛函 微分方程和抽象的沃尔泰拉方程， 控制和稳定问题的系统，由这种 方程 通过合作，将采用各种技术 应用于研究这些问题，包括：1）经典 分析方法，联合收割机技术开发的有限 双曲型技巧的三维沃尔泰拉方程 微分方程; 2）抽象方法，包括那些从 半群理论和非线性泛函分析; 3）半群 和对偶方法，其中一个无限维抽象方程 是近似有限维系统，数值研究 基于这种近似。 芬兰人的专业知识 谐波分析和能量方法的研究者， 对沃尔泰拉方程定性性质的研究应 称赞美国调查人员在功能方面的优势， 微分方程，控制理论和其他相关学科 提出的研究课题。 六名合作调查人员在以下方面享有盛誉： 专业知识和生产力在这一领域的应用数学。 他们三个人之间以前的互动是富有成果的。 显著 对数学的贡献可以从扩展的 两个研究小组之间的合作。

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.