On the Inverse Problem for a Size-Structured Population Model

Abstract

We consider a size-structured model for cell division and address the question of determining the division (birth) rate from the measured stable size distribution of the population. We formulate such question as an inverse problem for an integro-differential equation posed on the half line. We develop firstly a regular dependency theory for the solution in terms of the coefficients and, secondly, a novel regularization technique for tackling this inverse problem which takes into account the specific nature of the equation. Our results rely also on generalized relative entropy estimates and related Poincaré inequalities.

Cited by in corpus (15)

• Eigenelements of a General Aggregation-Fragmentation Model
• The contribution of age structure to cell population responses to targeted therapeutics
• Numerical Solution of an Inverse Problem in Size-Structured Population Dynamics
• Analysis of a Population Model Structured by the Cells Molecular Content
• Nonparametric estimation of the division rate of a size-structured population
• On the Calibration of a Size-Structured Population Model from Experimental Data
• Self-similarity in a General Aggregation-Fragmentation Problem ; Application to Fitness Analysis
• Estimating the division rate and kernel in the fragmentation equation
• A General Inverse Problem for the Growth-Fragmentation Equation
• The Shape of the Polymerization Rate in the Prion Equation
• High-order WENO scheme for Polymerization-type equations
• Adjoint method for a tumour growth PDE-constrained optimization problem
• Adjoint method for a tumor invasion PDE-constrained optimization problem using FEM
• A convergent numerical algorithm for the stochastic growth-fragmentation problem
• Adjoint method for a tumor invasion PDE-constrained optimization problem in 2D using Adaptive Finite Element Method