Q-well-posedness of an A$\beta$-protein polymerization model

Abstract

Abstract. 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.