Viscosity solutions for junctions: well posedness and stability
By Pierre-Louis Lions, Panagiotis E. Souganidis. 2016
64 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Statistical and Nonlinear Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/cc19409fd4d50954eab10b62df4de77b2f237e2a
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In Computational Theory and Mathematics
- Panagiotis E. Souganidis
- Pierre-Louis Lions
- S. Armstrong
- Russell W. Schwab
- Björn Engquist
- Konstantinos Spiliopoulos
- Bruno Ziliotto
- Luis Caffarelli
In Statistical and Nonlinear Physics
- Panagiotis E. Souganidis
- Pierre-Louis Lions
- Russell W. Schwab
- Björn Engquist
- Luis Caffarelli
- S. Armstrong
In Statistics and Probability
Citations in the corpus
- Well posedness for multi-dimensional junction problems with Kirchoff-type conditions (2017, background): “A classical blow-up argument (see, for example, Jensen and Souganidis [9]) shows that a+H i(p) ≤ 0 for all p ∈ [pi, pi] and b+H i(q) ≥ 0 for all q ∈ [qi, qi].”