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In this paper we present a mathematical model for the aggregation and diffusion of Aβ amyloid in the brain affected by Alzheimer's disease, at the early stage of the disease. The model is based on a classical discrete Smoluchowski aggregation equation modified to take diffusion into account. We also describe a numerical scheme and discuss the results of the… (More)

In this paper we exhibit a finite element method fitting a suitable geometry naturally associated with a class of degenerate elliptic equations (usually called Grushin type equations) in a plane region, and we discuss the related error estimates.

- Michiel Bertsch, Bruno Franchi, Norina Marcello, Maria Carla
- 2015

In this paper we propose a mathematical model for the onset and progression of Alzheimer's disease based on transport and diffusion equations. We regard brain neurons as a continuous medium, and structure them by their degree of malfunctioning. Two different mechanisms are assumed to be relevant for the temporal evolution of the disease: i) diffusion and… (More)

This paper completes a previous work on a Black and Scholes equation with stochastic volatility. This is a degenerate parabolic equation, which gives the price of a European option as a function of the time, of the price of the underlying asset, and of the volatility, when the volatility is a function of a mean reverting Orstein–Uhlenbeck process, possibly… (More)

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