STATE DETERMINATION IN DISTRIBUTIVE SYSTEMS WITH SPATIAL AVERAGING SENSORS,

Abstract

The problem of determining the initial data of a second-order parabolic partial-differential equation defined on a bounded spatial domain from an observation of the solution at a given time T > O is considered. The observation is in the form of a weighted spatial average of the solution at time T. Two sufficient conditions for the solvability of this problem are given. The first condition pertains to the form of the integral kernel involved in the observation and the second pertains to the smoothness of the initial data. The case where the observation is expressed in terms of a reproducing kernel of a Hilbert space is treated for the heat equation defined on a one-dimensional bounded spatial domain. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1969
Accession Number
AD0694087

Entities

People

  • Jean Claude Martin

Organizations

  • University of California, Los Angeles

Tags

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Hilbert Space
  • Integrals
  • Mathematical Analysis
  • Mathematics
  • Observation
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Climatology

Technology Areas

  • Space