Identification-Inverse Problems for Partial Differential Equations: A Stochastic Formulation.

Abstract

This paper presents a stochastic formulation of a class of identification problems for partial differential equations, known as 'inverse' problems in the mathematical-physics literature. By introducing stochastic processes to model errors in observation as well as 'disturbance' one can provide a precise formulation to interpret what appear to be 'ad hoc' techniques, especially in the treatment of 'inverse' problems. More importantly, one can model unknown sources as stochastic disturbances leading to more general 'inverse' problems than considered hitherto. The report deals only with Cauchy problems for partial differential equations with continuous time observation (as opposed to 'discrete' time). Topics discussed include the following: The white noise process; A class of inverse problems; Stochastic formulation; Stochastic formulation continued: source noise.

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1974
Accession Number
ADA001933

Entities

People

  • A.V. Balakrishnan

Organizations

  • University of California, Los Angeles

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Cauchy Problem
  • Differential Equations
  • Equations
  • Identification
  • Inverse Problems
  • Noise
  • Observation
  • Partial Differential Equations
  • Stochastic Processes
  • White Noise

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)