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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2510.14364 |
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| _version_ | 1866914096266346496 |
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| author | Ohavi, Isaac |
| author_facet | Ohavi, Isaac |
| contents | The aim of this work is to establish the well-posedness of fully nonlinear partial differential equations (PDE) posed on a star-shaped network, having nonlinear Kirchhoff's boundary condition at the vertex, and possibly degenerate. We obtain a comparison theorem, for discontinuous viscosity solutions, following the recent ideas obtained by Ohavi for second order problems, building test functions at the vertex solutions of Eikonal equations with well-designed coefficients. Another strong result obtained in this contribution is to show that any generalized Kirchhoff's viscosity solution introduced by Lions-Souganidis, is indeed a Kirchhoff's viscosity solution. In other terms, the values of the Hamiltonians are not required at the vertex in the analysis of these types of PDE systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14364 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Viscosity solutions posed on star-shaped network with Kirchhoff's boundary condition: Well-posedness Ohavi, Isaac Analysis of PDEs The aim of this work is to establish the well-posedness of fully nonlinear partial differential equations (PDE) posed on a star-shaped network, having nonlinear Kirchhoff's boundary condition at the vertex, and possibly degenerate. We obtain a comparison theorem, for discontinuous viscosity solutions, following the recent ideas obtained by Ohavi for second order problems, building test functions at the vertex solutions of Eikonal equations with well-designed coefficients. Another strong result obtained in this contribution is to show that any generalized Kirchhoff's viscosity solution introduced by Lions-Souganidis, is indeed a Kirchhoff's viscosity solution. In other terms, the values of the Hamiltonians are not required at the vertex in the analysis of these types of PDE systems. |
| title | Viscosity solutions posed on star-shaped network with Kirchhoff's boundary condition: Well-posedness |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.14364 |