Well posedness for multi-dimensional junction problems with Kirchoff-type conditions

@inproceedings{Lions2017WellPF,
  title={Well posedness for multi-dimensional junction problems with Kirchoff-type conditions},
  author={Pierre-Louis Lions and Panagiotis E. Souganidis},
  year={2017}
}
We consider multi-dimensional junction problems for first- and second-order pde with Kirchoff-type Neumann boundary conditions and we show that their generalized viscosity solutions are unique. It follows that any viscosity-type approximation of the junction problem converges to a unique limit. The results here are the first of this kind and extend previous work by the authors for one-dimensional junctions. The proofs are based on a careful analysis of the behavior of the viscosity solutions… CONTINUE READING

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