Estimating the division rate for the growth-fragmentation equation

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 par...

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Bibliographic Details
Published in:Journal of mathematical biology 2013-07, Vol.67 (1), p.69-103
Main Authors: Doumic, M., Tine, Léon M.
Format: Article
Language:English
Subjects:
Analysis of PDEs
Applications of Mathematics
Cell Division - physiology
Mathematical and Computational Biology
Mathematical Concepts
Mathematics
Mathematics and Statistics
Models, Biological
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Summary: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.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-012-0553-6