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Journal of Mathematical Biology

, Volume 67, Issue 1, pp 69–103 | Cite as

Estimating the division rate for the growth-fragmentation equation

  • M. DoumicEmail author
  • Léon M. Tine
Article

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.

Keywords

Growth-fragmentation equation Cell division equation General fragmentation kernels Inverse problem Eigenvalue problem 

Mathematics Subject Classification

35Q92 35R30 45Q05 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.INRIA Paris-Rocquencourt, EPI BANGLe Chesnay CedexFrance
  2. 2.Laboratoire d’Analyse Numérique et d’Informatique (LANI)Université Gaston BergerSaint-LouisSenegal
  3. 3.Labo P. Painlevé UMR 8524 CNRS, Université des Scienceset TechnologiesLille 1France
  4. 4.Project-Team SIMPAF, INRIA Lille Nord Europe Research CenterVilleneuve d’Ascq CedexFrance

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