English

Viscosity solutions for junctions: well posedness and stability

Analysis of PDEs 2016-08-15 v1

Abstract

We introduce a notion of state-constraint viscosity solutions for one dimensional \junction"-type problems for Hamilton-Jacobi equations with non convex coercive Hamiltonians and study its well- posedness and stability properties. We show that viscosity approximations either select the state- constraint solution or have a unique limit. We also introduce another type of approximation by fattening the domain. We also make connections with existing results for convex equations and discuss extensions to time dependent and/or multi-dimensional problems.

Keywords

Cite

@article{arxiv.1608.03682,
  title  = {Viscosity solutions for junctions: well posedness and stability},
  author = {P. -L. Lions and P. E. Souganidis},
  journal= {arXiv preprint arXiv:1608.03682},
  year   = {2016}
}

Comments

9 pages

R2 v1 2026-06-22T15:18:13.715Z