Moments approaches for asymptotic inverse problems of depolymerisation and fragmentation systems
Résumé
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-D\"oring 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.
Mots clés
Fragmentation equation
Asymptotic analysis 2010 MSC 35Q83
Inverse problems
Depolymerisation
Long-time dynamics
short-time dynamics
Depolymerisation system observability inequality Carleman inequalities error estimates Tikhonov regularisation Moments methods Measure-valued solutions Fragmentation equation. 2020 Mathematics Subject Classification: 35R30 35A35 35A23 35C10 35D30 35R0935Q92 92D25
Depolymerisation system
observability inequality
Carleman inequalities
error estimates
Tikhonov regularisation
Moments methods
Measure-valued solutions
Fragmentation equation. 2020 Mathematics Subject Classification: 35R30
35A35
35A23
35C10
35D30
35R0935Q92
92D25
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