Homogenization of fully overdamped Frenkel-Kontorova models

DOI10.1016/j.jde.2008.06.034zbMath1171.49023OpenAlexW2015864400MaRDI QIDQ2378615

Cyril Imbert, Nicolas Forcadel, Régis Monneau

Publication date: 13 January 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.06.034

zbMATH Keywords

Hamilton-Jacobi equationsperiodic homogenizationparticle systemscumulative distribution functionFrenkel-Kontorova modelsSlepčev formulationHull function

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Periodic solutions to PDEs (35B10) Nonlinear first-order PDEs (35F20) Discrete version of topics in analysis (39A12) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Integro-differential operators (47G20)

Related Items (24)

Traveling solutions for a multi-anticipative car-following traffic model ⋮ Variational modeling of dislocations in crystals in the line-tension limit ⋮ Dislocation dynamics: from microscopic models to macroscopic crystal plasticity ⋮ Specified homogenization of a discrete traffic model leading to an effective junction condition ⋮ Reduced ODE dynamics as formal relativistic asymptotics of a Peierls–Nabarro model ⋮ Existence and uniqueness of traveling waves for fully overdamped Frenkel-Kontorova models ⋮ The velocity diagram for traveling waves ⋮ Traveling waves for discrete reaction-diffusion equations in the general monostable case ⋮ Invariance and homogenization of an adaptive time gap car-following model ⋮ Velocity diagram of traveling waves for discrete reaction-diffusion equations ⋮ Semidiscrete shocks for the full velocity difference model ⋮ Homogenization of the Peierls-Nabarro model for dislocation dynamics ⋮ The Peierls-Nabarro model as a limit of a Frenkel-Kontorova model ⋮ Existence and uniqueness of traveling wave for accelerated Frenkel-Kontorova model ⋮ Derivation of Orowan's Law from the Peierls–Nabarro Model ⋮ Homogenization of second order discrete model with local perturbation and application to traffic flow ⋮ Numerical homogenization of a second order discrete model for traffic flow ⋮ Diffusion as a singular homogenization of the Frenkel-Kontorova model ⋮ From Heterogeneous Microscopic Traffic Flow Models to Macroscopic Models ⋮ Homogenization of a discrete model for a bifurcation and application to traffic flow ⋮ Homogenization of accelerated Frenkel-Kontorova models with $n$ types of particles ⋮ A non-local macroscopic model for traffic flow ⋮ Stochastic homogenization of Hamilton-Jacobi equations on a junction ⋮ Dynamics of discrete screw dislocations on glide directions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
• Homogenization of some particle systems with two-body interactions and of the dislocation dynamics
• Viscosity solutions of Hamilton-Jacobi equations
• Some homogenization results for non-coercive Hamilton-Jacobi equations
• Homogenization of first-order equations with \((u/\varepsilon)\)-periodic Hamiltonians. I: Local equations
• Rotation number of the overdamped Frenkel-Kontorova model with ac-driving
• Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenization of Hamilton-Jacobi equations
• User’s guide to viscosity solutions of second order partial differential equations
• The perturbed test function method for viscosity solutions of nonlinear PDE

This page was built for publication: Homogenization of fully overdamped Frenkel-Kontorova models