46 citations · 131 across the 10 of their papers we have counts for
10 papers
The role of beta-amyloid and tau proteins in Alzheimer's disease: a mathematical model on graph
Michiel Bertsch, Bruno Franchi, Maria Carla Tesi +1
In this Note we study a mathematical model for the progression of Alzheimer's Disease in the human brain. The novelty of our approach consists in the representation of the brain as…
Discontinuous solutions of Hamilton-Jacobi equations versus Radon measure-valued solutions of scalar conservation laws: Disappearance of singularities
M. Bertsch, F. Smarrazzo, A. Terracina +1
Let be a bounded and Lipschitz continuous function. We consider discontinuous viscosity solutions of the Hamilton-Jacobi equation and signed Radon measure valu…
A sensitivity analysis of a mathematical model for the synergistic interplay of Amyloid beta and tau on the dynamics of Alzheimer's disease
Michiel Bertsch, Bruno Franchi, Valentina Meschini +2
We propose a mathematical model for the onset and progression of Alzheimer's disease based on transport and diffusion equations. We treat brain neurons as a continuous medium and s…
A free boundary problem for binary fluids
Roberto Benzi, Michiel Bertsch, Francesco Deangelis
A free boundary problem for the dynamics of a glasslike binary fluid naturally leads to a singular perturbation problem for a strongly degenerate parabolic partial differential equ…
A uniqueness criterion for measure-valued solutions of scalar hyperbolic conservation laws
Michiel Bertsch, Flavia Smarrazzo, Andrea Terracina +1
We prove existence and uniqueness of Radon measure-valued solutions of the Cauchy problem $$ \begin{cases} u_t+[φ(u)]_x=0 & \text{in } \mathbb{R}\times (0,T) \\ u=u_0\ge 0 &\text{i…
Radon measure-valued solutions of first order hyperbolic conservation laws
Michiel Bertsch, Flavia Smarrazzo, Andrea Terracina +1
We study nonnegative solutions of the Cauchy problem $$ \begin{cases} u_t+[φ(u)]_x=0 & \text{in } \mathbb{R}\times (0,T) \\ u=u_0\ge 0&\text{in } \mathbb{R}\times \{0\}, \end{cases…
Well-posedness of a mathematical model for Alzheimer's disease
Michiel Bertsch, Bruno Franchi, Maria Carla Tesi +1
We consider the existence and uniqueness of solutions of an initial-boundary value problem for a coupled system of PDE's arising in a model for Alzheimer's disease. Apart from reac…
Microscopic and macroscopic models for the onset and progression of Alzheimer's disease
Michiel Bertsch, Bruno Franchi, Maria Carla Tesi +1
In the first part of this paper we review a mathematical model for the onset and progression of Alzheimer's disease (AD) that was developed in subsequent steps over several years.…
Alzheimer's disease: a mathematical model for onset and progression
Michiel Bertsch, Bruno Franchi, Norina Marcello +2
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 continuo…
Self-Similar Intermediate Asymptotics for a Degenerate Parabolic Filtration-Absorption Equation
G. I. Barenblatt, M. Bertsch, A. E. Chertock +1
The equation is known in literature as a qualitative mathematical model of some biological phenomena. Here this equation is…