Geodesic
Q-well-posedness of an Aβ-protein polymerization model
Cheikh Gueye1, 2 ; Sorin I. Ciuperca3 ; Laurent Pujo-Menjouet1, 2 ; Léon Matar Tine1, 2
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
Mathematical modelling of natural phenomena, Tome 19 (2024), article no. 19 Cet article a éte moissonné depuis la source EDP Sciences

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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.
DOI : 10.1051/mmnp/2023028

Cheikh Gueye 1, 2 ; Sorin I. Ciuperca 3 ; Laurent Pujo-Menjouet 1, 2 ; Léon Matar Tine 1, 2

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 
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Cheikh Gueye; Sorin I. Ciuperca; Laurent Pujo-Menjouet; Léon Matar Tine. Q-well-posedness of an Aβ-protein polymerization model. Mathematical modelling of natural phenomena, Tome 19 (2024), article  no. 19. doi: 10.1051/mmnp/2023028

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