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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2410.08430 |
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| _version_ | 1866929537662582784 |
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| author | Ishige, Kazuhiro Katayama, Sho Kawakami, Tatsuki |
| author_facet | Ishige, Kazuhiro Katayama, Sho Kawakami, Tatsuki |
| contents | We give an explicit representation of the fundamental solution to the heat equation on a half-space of ${\mathbb R}^N$ with the homogeneous dynamical boundary condition, and obtain upper and lower estimates of the fundamental solution. These enable us to obtain sharp decay estimates of solutions to the heat equation with the homogeneous dynamical boundary condition. Furthermore, as an application of our decay estimates, we identify the so-called Fujita exponent for a semilinear heat equation on the half-space of ${\mathbb R}^N$ with the homogeneous dynamical boundary condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08430 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fundamental solution to the heat equation with a dynamical boundary condition Ishige, Kazuhiro Katayama, Sho Kawakami, Tatsuki Analysis of PDEs We give an explicit representation of the fundamental solution to the heat equation on a half-space of ${\mathbb R}^N$ with the homogeneous dynamical boundary condition, and obtain upper and lower estimates of the fundamental solution. These enable us to obtain sharp decay estimates of solutions to the heat equation with the homogeneous dynamical boundary condition. Furthermore, as an application of our decay estimates, we identify the so-called Fujita exponent for a semilinear heat equation on the half-space of ${\mathbb R}^N$ with the homogeneous dynamical boundary condition. |
| title | Fundamental solution to the heat equation with a dynamical boundary condition |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.08430 |