Numerical Schemes for Conservation Laws via Hamilton-Jacobi Equations

DOI10.2307/2153439zbMath0827.65085OpenAlexW2039241950MaRDI QIDQ4846007

Lucilla Corrias, Roberto Natalini, Maurizio Falcone

Publication date: 11 December 1995

Full work available at URL: https://doi.org/10.2307/2153439

zbMATH Keywords

comparisonconvergenceHamilton-Jacobi equationentropy solutionconservation lawfinite differenceviscosity solutionsentropy weak solutions

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items

A note on front tracking and the equivalence between viscosity solutions of Hamilton-Jacobi equations and entropy solutions of scalar conservation laws, Godunov-type numerical methods for a model of granular flow, Fifth-order weighted power-ENO schemes for Hamilton-Jacobi equations, Initial data identification in conservation laws and Hamilton-Jacobi equations, Solving 1D conservation laws using Pontryagin's minimum principle, Hamilton-Jacobi and fractional like action with time scaling, On numerical approximation of the Hamilton-Jacobi-transport system arising in high frequency approximations, Existence of viscosity solution for a singular Hamilton-Jacobi equation, Unconditionally stable methods for Hamilton-Jacobi equations, Time periodic optimal policy for operation of a water storage tank using the dynamic programming approach, Existence and uniqueness for a nonlinear parabolic/Hamilton-Jacobi coupled system describing the dynamics of dislocation densities, Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains, New high-resolution semi-discrete central schemes for Hamilton-Jacobi equations, Overcoming the curse of dimensionality for some Hamilton-Jacobi partial differential equations via neural network architectures, Semi-Lagrangian schemes for Hamilton-Jacobi equations, discrete representation formulae and Godunov methods, Value iteration convergence of \(\varepsilon\)-monotone schemes for stationary Hamilton-Jacobi equations

Cites Work

• A numerical approach to the infinite horizon problem of deterministic control theory
• High resolution schemes for hyperbolic conservation laws
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Two Approximations of Solutions of Hamilton-Jacobi Equations
• Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations
• On Hopf's formulas for solutions of Hamilton-Jacobi equations
• A large Time Step Generalization of Godunov’s Method for Systems of Conservation Laws
• Riemann Solvers, the Entropy Condition, and Difference
• On a Large Time-Step High Resolution Scheme
• Viscosity Solutions of Hamilton-Jacobi Equations
• Scalar conservation laws and Hamilton-Jacobi equations in one-space variable
• User’s guide to viscosity solutions of second order partial differential equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item