Green functions for the heat and Laplace equations with dynamical boundary conditions in a ball
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918191342551040 |
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| author | Yang, Xuzhou |
| author_facet | Yang, Xuzhou |
| contents | The green functions for the heat and Laplace equations with dynamical boundary conditions in a ball are studied. First, the green functions of the Laplace equation with a dynamical boundary condition are given, and the properties of related heat kernels are discussed. Then using these ingredients, two complementary approximations to the heat equation with a dynamical boundary condition in a ball are constructed, including an approximation of green function and an approximation of solution. Moreover, the green function of the heat equation with a dynamical boundary condition is implicitly presented by a series of eigenfunctions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09413 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Green functions for the heat and Laplace equations with dynamical boundary conditions in a ball Yang, Xuzhou Analysis of PDEs Primary 35K05, Secondary 35K08, 35K20, 35E05, 35J08 The green functions for the heat and Laplace equations with dynamical boundary conditions in a ball are studied. First, the green functions of the Laplace equation with a dynamical boundary condition are given, and the properties of related heat kernels are discussed. Then using these ingredients, two complementary approximations to the heat equation with a dynamical boundary condition in a ball are constructed, including an approximation of green function and an approximation of solution. Moreover, the green function of the heat equation with a dynamical boundary condition is implicitly presented by a series of eigenfunctions. |
| title | Green functions for the heat and Laplace equations with dynamical boundary conditions in a ball |
| topic | Analysis of PDEs Primary 35K05, Secondary 35K08, 35K20, 35E05, 35J08 |
| url | https://arxiv.org/abs/2503.09413 |