Convergence of approximation schemes for nonlocal front propagation equations
DOI10.1090/S0025-5718-09-02270-4zbMath1208.65138OpenAlexW2021343279MaRDI QIDQ3584770
Publication date: 30 August 2010
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0025-5718-09-02270-4
convergenceviscosity solutionssecond-order equationsdislocation dynamicslevel-set approachFitzHugh-Nagumo systemnonlocal Hamilton-Jacobi equations\(L^1\) dependence in timefront propagations
Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Hamilton-Jacobi equations in mechanics (70H20) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Hamilton-Jacobi equations (35F21)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations
- Viscosity solutions of fully nonlinear second order parabolic equations with \(L^1\) dependence in time and Neumann boundary conditions
- Viscosity solutions of fully nonlinear second order parabolic equations with \(L^1\) dependence in time and Neumann boundary conditions. Existence and applications to the level-set approach
- Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
- Uniqueness of viscosity solutions of fully nonlinear second order parabolic equations with discontinuous time-dependence
- Level set methods and dynamic implicit surfaces
- Approximation schemes for propagation of fronts with nonlocal velocities and Neumann boundary conditions
- A convergent scheme for a nonlocal Hamilton Jacobi equation modelling dislocation dynamics
- Dislocation dynamics: Short-time existence and uniqueness of the solution
- A new stability result for viscosity solutions of nonlinear parabolic equations with weak convergence in time
- On the approximation of front propagation problems with nonlocal terms
- Global Existence Results and Uniqueness for Dislocation Equations
- Global Existence of Weak Solutions for Interface Equations Coupled with Diffusion Equations
- Existence and uniqueness of unbounded viscosity solutions of parabolic equations with discontinuous time-dependence
- A Simple Proof of Convergence for an Approximation Scheme for Computing Motions by Mean Curvature
- Phase-Field Theory for FitzHugh–Nagumo-Type Systems
This page was built for publication: Convergence of approximation schemes for nonlocal front propagation equations