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arXiv · 1608.03682

Viscosity solutions for junctions: well posedness and stability

P. -L. Lions·P. E. Souganidis
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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.

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P. -L. Lions, P. E. Souganidis. 2016-08-12. Viscosity solutions for junctions: well posedness and stability. https://arxiv.org/abs/1608.03682

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