An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations.
We investigate the inverse problem of identifying a conditional probability measure in measure-dependent evolution equations arising in size-structured population modeling. We formulate the inverse problem as a least squares problem for the probability measure estimation. Using the Prohorov metric framework, we prove existence and consistency of the least squares estimates and outline a discretization scheme for approximating a conditional probability 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.
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309-0526.
Inom
I
Mirzaev
The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760.
Erin C
EC
Byrne
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309-0526.
David M
DM
Bortz
Conditional probability measures; bacterial aggregates; flocculation; fragmentation; inverse problem; measure-dependent evolution equations; size-structured populations