From a microscopic to a macroscopic model for Alzheimer disease: two-scale homogenization of the Smoluchowski equation in perforated domains

DOI10.1007/s00332-016-9288-7zbMath1342.35408OpenAlexW2280916133MaRDI QIDQ295319

Silvia Lorenzani, Bruno Franchi

Publication date: 13 June 2016

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/11585/553702

zbMATH Keywords

homogenizationSmoluchowski equationAlzheimer diseaseneuron membranes

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Medical applications (general) (92C50) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items

Bifurcation Analysis and Finite-Time Contraction Stability of an Alzheimer Disease Model, Homogenization of the discrete diffusive coagulation-fragmentation equations in perforated domains, The role of \(\mathrm{A}\beta\) and tau proteins in Alzheimer's disease: a mathematical model on graphs, Microscopic and macroscopic models for the onset and progression of Alzheimer's disease, Discontinuous Galerkin methods for Fisher-Kolmogorov equation with application to \(\alpha\)-synuclein spreading in Parkinson's disease, Smoluchowski Equation with Variable Coefficients in Perforated Domains: Homogenization and Applications to Mathematical Models in Medicine, Well-Posedness of a Mathematical Model for Alzheimer's Disease, Unnamed Item, Stability analysis of a bulk-surface reaction model for membrane protein clustering, The amyloid cascade hypothesis and Alzheimer’s disease: A mathematical model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Alzheimer's disease: analysis of a mathematical model incorporating the role of prions
• Homogenization of nonlinear reaction-diffusion equation with a large reaction term
• Mass-conserving solutions and non-conservative approximation to the Smoluchowski coagulation equation
• Global solutions of reaction-diffusion systems
• Diffusion, convection, adsorption, and reaction of chemicals in porous media
• On the application of the homogenization theory to a class of problems arising in fluid mechanics
• Miscible displacement in porous media influenced by mobile and immobile water
• Homogenization of reticulated structures
• Existence of solutions for the discrete coagulation-fragmentation model with diffusion
• Global existence for the discrete diffusive coagulation-fragmentation equations in \(L^1\).
• Global existence for the continuous nonhomogeneous Smoluchowski equation and asymptotic behaviour of the solutions
• Homogenization of a parabolic equation in perforated domain with Neumann boundary condition
• Steklov problems in perforated domains with a coefficient of indefinite sign
• A qualitative model for aggregation and diffusion of \(\beta \)-amyloid in Alzheimer's disease
• Homogenization and Two-Scale Convergence
• A General Convergence Result for a Functional Related to the Theory of Homogenization
• Which sequences of holes are admissible for periodic homogenization with Neumann boundary condition?
• Microscopic and macroscopic models for the onset and progression of Alzheimer's disease
• Numerical Simulation of the Smoluchowski Coagulation Equation
• Γ-convergence approach to variational problems in perforated domains with Fourier boundary conditions
• Inhomogeneous parabolic Neumann problems
• Random heterogeneous materials. Microstructure and macroscopic properties