Moments approaches for asymptotic inverse problems of depolymerisation and fragmentation systems
[In collaboration with Miguel Escobedo, Philippe Moireau and Magali Tournus]
Marie Doumic1
1 MERGE, CMAP, Inria, IP Paris, Ecole polytechnique, CNRS, 91128 Palaiseau cedex FRANCE
Journées équations aux dérivées partielles (2023), Exposé no. 4, 13 p.

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.

Publié le :
DOI : 10.5802/jedp.675
Classification : 35R30, 35A35, 35A23, 35C10, 35D30, 35R09, 35Q92, 92D25
Keywords: Depolymerisation system, observability inequality, Carleman inequalities, error estimates, Tikhonov regularisation, Moments methods, Measure-valued solutions, Fragmentation equation

Marie Doumic 1

1 MERGE, CMAP, Inria, IP Paris, Ecole polytechnique, CNRS, 91128 Palaiseau cedex FRANCE 
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Marie Doumic. Moments approaches for asymptotic inverse problems of depolymerisation and fragmentation systems. Journées équations aux dérivées partielles (2023), Exposé no. 4, 13 p. doi : 10.5802/jedp.675. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.675/

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