Viscosity solutions for junctions: well posedness and stability
Pierre-Louis Lions
Université de Paris-Dauphine, Paris, FrancePanagiotis E. Souganidis
University of Chicago, USA
![Viscosity solutions for junctions: well posedness and stability cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rlm-volume-27-issue-4.png&w=3840&q=90)
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