Effective nonlinear Neumann boundary conditions for 1D nonconvex Hamilton-Jacobi equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Guerand, Jessica¹ 

[1] PSL Res Univ, Dept Math & Applicat, Ecole Normale Super, CNRS, 45 Rue Ulm, F-75005 Paris, France

关键词: Hamilton-Jacobi equations;    Nonconvex Hamiltonians;    Discontinuous Hamiltonians;    Viscosity solutions;    Comparison principle;    Effective boundary conditions;   

DOI  :  10.1016/j.jde.2017.04.015

来源: Elsevier

【 摘 要 】

We study Hamilton-Jacobi equations in [0, +infinity) of evolution type with nonlinear Neumann boundary conditions in the case where the Hamiltonian is not necessarily convex with respect to the gradient variable. In this paper, we give two main results. First, we prove for a nonconvex and coercive Hamiltonian that general boundary conditions in a relaxed sense are equivalent to effective ones in a strong sense. Here, we exhibit the effective boundary conditions while for a quasi-convex Hamiltonian, we already know them (Imbert and Monneau, 2016). Second, we give a comparison principle for a nonconvex and nonnecessarily coercive Hamiltonian where the boundary condition can have constant parts. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free