Inverse Problems for a Class of Conditional Probability Measure-Dependent Evolution Equations
Statistics Theory
2015-10-07 v1 Analysis of PDEs
Functional Analysis
Optimization and Control
Statistics Theory
Abstract
We investigate the inverse problem of identifying a conditional probability measure in a measure-dependent dynamical system. We provide existence and well-posedness results and outline a discretization scheme for approximating a measure. For this scheme, we prove general method stability. The work is motivated by Partial Differential Equation (PDE) models of flocculation for which the shape of the post-fragmentation conditional probability measure greatly impacts the solution dynamics. To illustrate our methodology, we apply the theory to a particular PDE model that arises in the study of population dynamics for flocculating bacterial aggregates in suspension, and provide numerical evidence for the utility of the approach.
Cite
@article{arxiv.1510.01355,
title = {Inverse Problems for a Class of Conditional Probability Measure-Dependent Evolution Equations},
author = {David M. Bortz and Erin C. Byrne and Inom Mirzaev},
journal= {arXiv preprint arXiv:1510.01355},
year = {2015}
}