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