An inverse problem for a class of conditional probability measure-dependent evolution equations. (15th July 2016)

• Record Type: Journal Article
• Authors: Mirzaev, Inom; Byrne, Erin C; Bortz, David M
• Is Part Of: Inverse problems. Volume 32:Number 9(2016:Sep.)
• Publication Date: 2016-07-15
• Subjects: inverse problem -- size-structured populations -- flocculation -- fragmentation -- bacterial aggregates -- conditional probability measures -- measure-dependent evolution equations; 35Q92 -- 35R30 -- 65M32 -- 92D25; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/9/095005
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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 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.