Browsing by Author "Franchi, Bruno"
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- ItemHeat Kernels, Stochastic Processes and Functional Inequalities(Zürich : EMS Publ. House, 2005) Franchi, Bruno; Kumagai, Takashi; Sturm, Karl-TheodorThe conference brought together mathematicians belonging to several fields, essentially analysis, probability and geometry. One of the main unifying topics was certainly the study of heat kernels in various contexts: fractals, manifolds, domains of the Euclidean space, percolation clusters, infinite dimensional spaces, metric measure spaces.
- ItemA mathematical model for Alzheimer's disease: An approach via stochastic homogenization of the Smoluchowski equation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Franchi, Bruno; Heida, Martin; Lorenzani, SilviaIn this note, we apply the theory of stochastic homogenization to find the asymptotic behavior of the solution of a set of Smoluchowski's coagulation-diffusion equations with non-homogeneous Neumann boundary conditions. This system is meant to model the aggregation and diffusion of β-amyloid peptide (Aβ) in the cerebral tissue, a process associated with the development of Alzheimer's disease. In contrast to the approach used in our previous works, in the present paper we account for the non-periodicity of the cellular structure of the brain by assuming a stochastic model for the spatial distribution of neurons. Further, we consider non-periodic random diffusion coefficients for the amyloid aggregates and a random production of Aβ in the monomeric form at the level of neuronal membranes.