Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics
From MaRDI portal
Publication:952515
DOI10.4171/JEMS/140zbMath1158.35324OpenAlexW2132295481MaRDI QIDQ952515
Régis Monneau, Francesca Da Lio, Nicolas Forcadel
Publication date: 12 November 2008
Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)
Full work available at URL: http://www.ems-ph.org/journals/show_pdf.php?issn=1435-9855&vol=10&iss=4&rank=8
Asymptotic behavior of solutions to PDEs (35B40) Initial value problems for nonlinear higher-order PDEs (35G25) Initial value problems for nonlinear first-order PDEs (35F25) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)
Related Items
Convergence of nonlocal threshold dynamics approximations to front propagation ⋮ A posteriori error estimates for the effective Hamiltonian of dislocation dynamics ⋮ A nonlocal convection-diffusion equation ⋮ The core-radius approach to supercritical fractional perimeters, curvatures and geometric flows ⋮ Stability results for nonlocal geometric evolutions and limit cases for fractional mean curvature flows ⋮ Homogenization of second order discrete model with local perturbation and application to traffic flow ⋮ Well-posedness and numerical analysis of a one-dimensional non-local transport equation modelling dislocations dynamics ⋮ Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting ⋮ Convergence of nonlocal geometric flows to anisotropic mean curvature motion ⋮ Homogenization of a discrete model for a bifurcation and application to traffic flow ⋮ Asymptotic expansions for nonlocal diffusion equations in \(L^q\)-norms for \(1\leqslant q\leqslant 2\)
Cites Work
- Unnamed Item
- The self-force on a planar dislocation loop in an anisotropic linear- elastic medium
- Viscosity solutions of Hamilton-Jacobi equations
- Minimal barriers for geometric evolutions
- A new approach to front propagation problems: theory and applications
- Small-time solvability of a non-local Hamilton-Jacobi equation describing dislocation dynamics
- Existence and uniqueness for dislocation dynamics with nonnegative velocity
- A convergent scheme for a nonlocal Hamilton Jacobi equation modelling dislocation dynamics
- Convergence of a first order scheme for a nonlocal eikonal equation
- Dislocation dynamics: Short-time existence and uniqueness of the solution
- Exit Time Problems in Optimal Control and Vanishing Viscosity Method
- Front Propagation and Phase Field Theory
- A Simple Proof of Convergence for an Approximation Scheme for Computing Motions by Mean Curvature
- The self-stress of dislocations and the shape of extended nodes
- Nonlocal First-Order Hamilton–Jacobi Equations Modelling Dislocations Dynamics
- Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
- Sharp interface limits for non-local anisotropic interactions
