A convergent scheme for a non-local coupled system modelling dislocations densities dynamics

DOI10.1090/S0025-5718-07-02038-8zbMath1133.35097OpenAlexW2029846275MaRDI QIDQ5444306

Nicolas Forcadel, Ahmad El Hajj

Publication date: 25 February 2008

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-07-02038-8

zbMATH Keywords

Hamilton-Jacobi equationserror estimatenumerical schemeviscosity solutionsCrandall-Lionsdislocations densities dynamics

Mathematics Subject Classification ID

Numerical approximation of solutions of dynamical problems in solid mechanics (74H15) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items

Short time existence and uniqueness in Hölder spaces for the 2D dynamics of dislocation densities ⋮ Global \(BV\) solution for a non-local coupled system modeling the dynamics of dislocation densities ⋮ Formal derivation and existence result of an approximate model on dislocation densities ⋮ Entropy solutions to a non-conservative and non-strictly hyperbolic diagonal system inspired by dislocation dynamics ⋮ A posteriori error estimates for the effective Hamiltonian of dislocation dynamics ⋮ GLOBAL CONTINUOUS SOLUTIONS FOR DIAGONAL HYPERBOLIC SYSTEMS WITH LARGE AND MONOTONE DATA ⋮ Global existence for a system of nonlinear and non-local transport equations describing the dynamics of dislocation densities ⋮ Existence and uniqueness of continuous solution for a non-local coupled system modeling the dynamics of dislocation densities ⋮ \(BV\) solution for a non-linear Hamilton-Jacobi system ⋮ Convergence of an implicit scheme for diagonal non-conservative hyperbolic systems ⋮ Time-homogenization of a first order system arising in the modelling of the dynamics of dislocation densities ⋮ Convergence and non-convergence of many-particle evolutions with multiple signs ⋮ Existence and uniqueness for a nonlinear parabolic/Hamilton-Jacobi coupled system describing the dynamics of dislocation densities ⋮ Continuous solution for a non-linear eikonal system ⋮ Dynamics of Dislocation Densities in a Bounded Channel. Part II: Existence of Weak Solutions to a Singular Hamilton–Jacobi/Parabolic Strongly Coupled System ⋮ Global existence to a diagonal hyperbolic system for any BV initial data ⋮ UNIQUENESS RESULTS FOR DIAGONAL HYPERBOLIC SYSTEMS WITH LARGE AND MONOTONE DATA ⋮ Convergent semi-explicit scheme to a non-linear eikonal system

Cites Work

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• Dislocation dynamics with a mean curvature term: short time existence and uniqueness.
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Viscosity solutions for weakly coupled systems of first-order partial differential equations
• Perron's method for monotone systems of second-order elliptic partial differential equations
• Viscosity solutions of Hamilton-Jacobi equations
• A Hamilton-Jacobi equation with measures arising in \(\Gamma \)-convergence of optimal control problems
• 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
• Convergence rates for semi-discrete splitting approximations for degenerate parabolic equations with source teams
• On the Convergence Rate ofOperator Splitting for Hamilton--Jacobi Equations with Source Terms
• Two Approximations of Solutions of Hamilton-Jacobi Equations
• Viscosity Solutions for Weakly Coupled Systems of Hamilton-Jacobi Equations
• Viscosity solutions for monotone systems of second–order elliptic PDES
• Viscosity solutions associated with switching game for piecewise-deterministic processes
• A Viscosity Solutions Approach to Shape-From-Shading
• User’s guide to viscosity solutions of second order partial differential equations
• A System of Nonlinear Partial Differential Equations Arising in the Optimal Control of Stochastic Systems with Switching Costs
• Nonlocal First-Order Hamilton–Jacobi Equations Modelling Dislocations Dynamics
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations