Accession Number : ADA132821

Title :   Stabilization of Solutions for a Class of Parabolic Integro-Differential Equations.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Engler,Hans

PDF Url : ADA132821

Report Date : Aug 1983

Pagination or Media Count : 56

Abstract : Integro-differential equations arise in the description of feed-back control systems, where the control variables are derived from filtered observations of the state or where the control mechanism possesses inertia. The author studies a model equation for a distributed control system (e.g., the state varies over some space-like domain) which contains also some diffusion effects and give conditions under which the state will tend to some limit, as time goes to infinity, regardless of the initial situation. The limit is shown to satisfy an elliptic differential equation. Convergence rates are also given; these show the slowing-down effect of a slow control mechanism on the convergence of the state variable. The problem under study can also be viewed as a natural extension of a type of reaction-diffusion equation that has received wide attention in the literature. (Author)

Descriptors :   *Integral equations, *Differential equations, *Control systems, Feedback, Solutions(General), Stabilization, Asymptotic normality, Convergence, Rates, Diffusion, Variables, Boundary value problems, Theorems

Subject Categories : Numerical Mathematics
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Distribution Statement : APPROVED FOR PUBLIC RELEASE