Viscosity solutions for junctions: well posedness and stability

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- c...

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Bibliographic Details
Published inarXiv.org
Main Authors P -L Lions, Souganidis, P E
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.08.2016
Subjects
Coercivity
Dimensional stability
Mathematical analysis
Nonlinear equations
Time dependence
Viscosity
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Summary: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.
ISSN:2331-8422