Inverse Problems for a Class of Measure Dependent Dynamical Systems

Abstract

We consider a class of probability measure dependent dynamical systems which arise in the study of multiscale phenomena in diverse fields such as immunological population dynamics, viscoelasticity of polymers and rubber and polarization in dielectric materials. We develop an inverse problem framework for studying systems with distributed temporal delays. In particular, we establish conditions for existence and uniqueness of the forward problem and well-posedness (including method stability under numerical approximations) for the inverse problem of estimating the probability measures. We show that a motivating class of models of HIV infection dynamics satisfies all the conditions of our framework, thereby providing a theoretical foundation for inverse problem computations with these models.

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Document Details

Document Type
Technical Report
Publication Date
Sep 23, 2004
Accession Number
ADA444236

Entities

People

  • D. M. Bortz
  • H. Thomas Banks

Organizations

  • North Carolina State University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Computational Science
  • Computations
  • Convergence
  • Differential Equations
  • Dynamics
  • Equations
  • Infection
  • Inverse Problems
  • Materials
  • Mathematical Models
  • Mathematics
  • Models
  • Probability
  • Probability Distributions
  • Weak Convergence
  • Wound Infections

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Theoretical Analysis.