The vanishing viscosity limit for Hamilton–Jacobi equations on networks

The vanishing viscosity limit for Hamilton–Jacobi equations on networks

Viscosity approximation for Hamilton–Jacobi equations on networks with Kirchhoff conditions at junction points — convergence to the unique solution of the original problem. With Fabio Camilli and Claudio Marchi, 2013.

Preprint auf ArXiv

Authors: Fabio Camilli, Claudio Marchi, Dirk Schieborn

Journal: Journal of Differential Equations

Reference: arXiv:1207.6535

Year of publication: 2013

Abstract

For a Hamilton–Jacobi equation defined on a network, we introduce an approximation by vanishing viscosity. The elliptic equation is defined on the edges and is coupled at the junction nodes with Kirchhoff-type conditions. We prove that exactly one solution of this elliptic approximation exists, and show in particular that it converges, as the viscosity vanishes, to the unique solution of the original problem.