A comparison principle for Hamilton-Jacobi equations with discontinuous Hamiltonians

A Comparison Principle for Hamilton-jacobi Equations with Discontinuous Hamiltonians

We show a comparison principle for viscosity superand subsolutions to Hamilton-Jacobi equations with discontinuous Hamiltonians. The key point is that the Hamiltonian depends upon u and has a special structure. The supersolution must enjoy some additional regularity.

Discontinuous Galerkin for Hamilton - Jacobi Equations

Viscosity solutions of discontinuous Hamilton–Jacobi equations

We define viscosity solutions for the Hamilton–Jacobi equation φt = v(x, t)H(∇φ) in RN × (0,∞) where v is positive and bounded measurable and H is non-negative and Lipschitz continuous. Under certain assumptions, we establish the existence and uniqueness of Lipschitz continuous viscosity solutions. The uniqueness result holds in particular for those v which are independent of t and piecewise co...

A Discontinuous Galerkin Finite Element Method for Hamilton-Jacobi Equations

In this paper, we present a discontinuous Galerkin finite clement method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact ste...

A New Discontinuous Galerkin Method for Hamilton-Jacobi Equations

In this paper we propose a new local discontinuous Galerkin method to directly solve Hamilton-Jacobi equations. The scheme is a natural extension of the monotone scheme. For the linear case, the method is equivalent to the discontinuous Galerkin method for conservation laws. Thus, stability and error analysis are obtained under the framework of conservation laws. For both convex and nonconvex H...