Viscosity solutions for junctions: well posedness and stability

2016/08/12 by Lions, P. -L., Souganidis, P. E. · 2 citations
#35B51 #35F21 #49L20 #49L25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.03682

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.

Cited by

• Viscosity solutions posed on star-shaped network with Kirchhoff's boundary condition: Well-posedness
• Degenerate Elliptic PDEs on a Network with Kirchhoff Conditions

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