Classification of nonlinear boundary conditions for 1D nonconvex Hamilton-Jacobi equations

2016/09/28 by Guerand, Jessica
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1609.08867

Abstract

We study Hamilton-Jacobi equations in [0, +∞) of evolution type with nonlinear boundary conditions of Neumann type in the case where the Hamiltonian is non necessarily convex with respect to the gradient variable. In this paper, we give two main results. First, we prove a classification of boundary condition result for a nonconvex, coercive Hamiltonian, in the spirit of the flux-limited formulation for quasi-convex Hamilton-Jacobi equations on networks recently introduced by Imbert and Monneau. Second, we give a comparison principle for a nonconvex and noncoercive Hamiltonian where the boundary condition can have flat parts.

Related

• Neumann type boundary conditions for Hamilton-Jacobi equations
• Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions
• A PDE approach to large-time asymptotics for boundary-value problems for nonconvex Hamilton-Jacobi Equations
• Non-convex Hamilton-Jacobi equations with gradient constraints
• Existence, Uniqueness and Asymptotic Behavior for Nonlocal Parabolic Problems with Dominating Gradient Terms