Nonlocal First-Order Hamilton–Jacobi Equations Modelling Dislocations Dynamics

DOI10.1080/03605300500361446zbMath1109.35026arXivmath/0603570OpenAlexW2004865639MaRDI QIDQ5491391

Olivier Ley, Guy Barles

Publication date: 11 October 2006

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603570

zbMATH Keywords

viscosity solutionslevel-set approachsemiconvexitygeometrical propertieslower-bound gradient estimatenonlocal front propagation

Mathematics Subject Classification ID

Nonlinear first-order PDEs (35F20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items

Uniqueness results for nonlocal Hamilton-Jacobi equations, Quasiconvexity preserving property for fully nonlinear nonlocal parabolic equations, A Dynamical Approach to Lower Gradient Estimates for Viscosity Solutions of Hamilton–Jacobi Equations, Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations, Lipschitz continuity and local semiconcavity for exit time problems with state constraints, Short time uniqueness results for solutions of nonlocal and non-monotone geometric equations, Global existence results for eikonal equation with \(BV\) initial data, Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics, Global solution for a non-local eikonal equation modelling dislocation dynamics, Existence result for a one-dimensional eikonal equation, Well-posedness and numerical analysis of a one-dimensional non-local transport equation modelling dislocations dynamics, Global existence for a system of nonlinear and non-local transport equations describing the dynamics of dislocation densities, Dislocation dynamics: Short-time existence and uniqueness of the solution, Minimizing movements for dislocation dynamics with a mean curvature term, A convergent scheme for a non-local coupled system modelling dislocations densities dynamics, Nonlocal second-order geometric equations arising in tomographic reconstruction, On Viscosity Solutions of Certain Hamilton–Jacobi Equations: Regularity Results and Generalized Sard's Theorems, Convergence of nonlocal geometric flows to anisotropic mean curvature motion

Cites Work

• Semiconcave functions, Hamilton-Jacobi equations, and optimal control
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Semiconcavity of the value function for exit time problems with nonsmooth target
• Approximation schemes for propagation of fronts with nonlocal velocities and Neumann boundary conditions
• Existence and uniqueness for dislocation dynamics with nonnegative velocity
• Interior sphere property of attainable sets and time optimal control problems
• Front Propagation and Phase Field Theory
• Unnamed Item
• Unnamed Item
• Unnamed Item