Global Results for Eikonal Hamilton-Jacobi Equations on Networks

Abstract

We study a one-parameter family of Eikonal Hamilton-Jacobi equations on an embedded network, and prove that there exists a unique critical value for which the corresponding equation admits global solutions, in a suitable viscosity sense. Such a solution is identified, via an Hopf-Lax type formula, once an admissible trace is assigned on an intrinsic boundary. The salient point of our method is to associate to the network an abstract graph, encoding all of the information on the complexity of the network, and to relate the differential equation to a discrete functional equation on the graph. Comparison principles and representation formulae are proven in the supercritical case as well.

46 pages

References in corpus (3)

• A junction condition by specified homogenization and application to traffic lights
• Quasi-convex Hamilton-Jacobi equations posed on junctions: The multi-dimensional case
• Convergence of discrete Aubry-Mather model in the continuous limit

Cited by in corpus (4)

• Lax--Oleinik formula on networks
• Aubry Set of Eikonal Hamilton-Jacobi Equations on Networks
• Large Time Behavior of Solutions to Hamilton-Jacobi Equations on Networks
• Numerical Approximation of the Critical Value of Eikonal Hamilton-Jacobi Equations on Networks