Estimating the division rate for the growth-fragmentation equation
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Updated: May 21, 2026

Kinematic Analysis of Cell Division and Expansion: Quantifying the Cellular Basis of Growth and Sampling Developmental Zones in Zea mays Leaves
Published on: December 2, 2016
1INRIA Paris-Rocquencourt, EPI BANG, Domaine de Voluceau, 78153, Le Chesnay Cedex, France. marie.doumic@inria.fr
Abstract:
Growth-fragmentation equations arise in many different contexts, ranging from cell division, protein polymerization, neurosciences etc. Direct observation of temporal dynamics being often difficult, it is of main interest to develop theoretical and numerical methods to recover reaction rates and parameters of the equation from indirect observation of the solution. Following the work done in Perthame and Zubelli (Inverse Probl 23:1037-1052, 2007) and Doumic et al. (2009) for the specific case of the cell division equation, we address here the general question of recovering the fragmentation rate of the equation from the observation of the time-asymptotic solution, when the fragmentation kernel and the growth rates are fully general. We give both theoretical results and numerical methods, and discuss the remaining issues.
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