Comparison principle for Walsh's spider HJB equations with non linear local time Kirchhoff's boundary transmission
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909469711007744 |
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| author | Ohavi, Isaac |
| author_facet | Ohavi, Isaac |
| contents | The main purpose of this work is to obtain a comparison principle for viscosity solutions of a system of elliptic Walsh's spider Hamilton-Jacobi-Bellman equations, possessing a new boundary condition called non linear local-time Kirchhoff's transmission. The main idea is to build test functions at the neighborhood of the vertex solutions of ODE, with well-designed coefficients. The key point is to impose a 'local-time' derivative at the vertex absorbing the error term induced by - what we decide to call here - the Kirchhoff's speed of the Hamiltonians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01362 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Comparison principle for Walsh's spider HJB equations with non linear local time Kirchhoff's boundary transmission Ohavi, Isaac Analysis of PDEs The main purpose of this work is to obtain a comparison principle for viscosity solutions of a system of elliptic Walsh's spider Hamilton-Jacobi-Bellman equations, possessing a new boundary condition called non linear local-time Kirchhoff's transmission. The main idea is to build test functions at the neighborhood of the vertex solutions of ODE, with well-designed coefficients. The key point is to impose a 'local-time' derivative at the vertex absorbing the error term induced by - what we decide to call here - the Kirchhoff's speed of the Hamiltonians. |
| title | Comparison principle for Walsh's spider HJB equations with non linear local time Kirchhoff's boundary transmission |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2312.01362 |