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.
