Viscosity solutions for junctions: well posedness and stability

  • Pierre-Louis Lions

    Université de Paris-Dauphine, Paris, France
  • Panagiotis E. Souganidis

    University of Chicago, USA

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, and we introduce another type of approximation by fattening the domain. We also make connections with existing results for convex equations and discuss extensions to time and/or multi-dimensional problems.

Cite this article

Pierre-Louis Lions, Panagiotis E. Souganidis, Viscosity solutions for junctions: well posedness and stability. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 27 (2016), no. 4, pp. 535–545

DOI 10.4171/RLM/747