Shrinkage of large particles, either through depolymerisation (i.e. progressive shortening) or through fragmentation (breakage into smaller pieces) may be modelled by discrete equations, of Becker–Döring type, or by continuous ones. In this note, we review two kinds of inverse problems: the first is the estimation of the initial size-distribution from moments measurements in a depolymerising system, in collaboration with Philippe Moireau and inspired by experiments carried out by Human Rezaei’s team; the second is the inference of fragmentation characteristics from size distribution samples, in collaboration with Miguel Escobedo and Magali Tournus, based on biological questions and experiments of Wei-Feng Xue’s team.
Keywords: Depolymerisation system, observability inequality, Carleman inequalities, error estimates, Tikhonov regularisation, Moments methods, Measure-valued solutions, Fragmentation equation
Doumic, Marie 1
@incollection{JEDP_2023____A4_0,
author = {Doumic, Marie},
title = {Moments approaches for asymptotic inverse problems of depolymerisation and fragmentation systems},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
note = {talk:4},
pages = {1--13},
publisher = {R\'eseau th\'ematique AEDP du CNRS},
year = {2023},
doi = {10.5802/jedp.675},
language = {en},
url = {https://www.numdam.org/articles/10.5802/jedp.675/}
}
TY - JOUR AU - Doumic, Marie TI - Moments approaches for asymptotic inverse problems of depolymerisation and fragmentation systems JO - Journées équations aux dérivées partielles N1 - talk:4 PY - 2023 SP - 1 EP - 13 PB - Réseau thématique AEDP du CNRS UR - https://www.numdam.org/articles/10.5802/jedp.675/ DO - 10.5802/jedp.675 LA - en ID - JEDP_2023____A4_0 ER -
%0 Journal Article %A Doumic, Marie %T Moments approaches for asymptotic inverse problems of depolymerisation and fragmentation systems %J Journées équations aux dérivées partielles %Z talk:4 %D 2023 %P 1-13 %I Réseau thématique AEDP du CNRS %U https://www.numdam.org/articles/10.5802/jedp.675/ %R 10.5802/jedp.675 %G en %F JEDP_2023____A4_0
Doumic, Marie. Moments approaches for asymptotic inverse problems of depolymerisation and fragmentation systems. Journées équations aux dérivées partielles (2023), Talk no. 4, 13 p.. doi: 10.5802/jedp.675
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