Issue |
Math. Model. Nat. Phenom.
Volume 19, 2024
|
|
---|---|---|
Article Number | 19 | |
Number of page(s) | 23 | |
Section | Population dynamics and epidemiology | |
DOI | https://doi.org/10.1051/mmnp/2023028 | |
Published online | 07 October 2024 |
Q-well-posedness of an Aβ-protein polymerization model
1
Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR5208, Inria Lyon, Institut Camille Jordan, F-69603 Villeurbanne, France
2
Laboratoire de Mathématiques Appliquées, Université Cheikh Anta Diop de Dakar, Sénégal
3
Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR5208, Institut Camille Jordan, F-69603 Villeurbanne, France
* Corresponding author: leon-matar.tine@univ-lyon1.fr
Received:
9
March
2023
Accepted:
7
September
2023
In this work, we consider a Becker-Döring-like mathematical interaction model between Aβ-monomers and Aβ proto-oligomers playing an important role in Alzheimer’s disease. In this context, the clustering process where two or more Aβ-monomers spontaneously aggregate and form a seed of proto-oligomers is highlighted. We prove the quadratic well-posedness [4] of the problem associated with the estimation of clustering rate μ from measured data at different times.
Mathematics Subject Classification: 65L09 / 65J22 / 92B05
Key words: Q well-posedness / parameter estimation / inverse problem / polymerization process / Aβ-protein / Alzheimer’ disease
© The authors. Published by EDP Sciences, 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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