Lie point symmetries of the biharmonic heat equation on surfaces of revolution
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909630544740352 |
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| author | Nass, Aminu Ma'aruf Mpungu, Kassimu Nuruddeen, Rahmatullah Ibrahim |
| author_facet | Nass, Aminu Ma'aruf Mpungu, Kassimu Nuruddeen, Rahmatullah Ibrahim |
| contents | This paper uses Lie symmetry analysis to investigate the biharmonic heat equation on a generalized surface of revolution. We classify the Lie point symmetries associated with this equation, allowing for the identification of surfaces and the corresponding infinitesimal generators. In a significant move, we demonstrate that the biharmonic heat equation on a surface of revolution admits the same Lie symmetries as the harmonic heat equation on the same surface, highlighting a profound structural relationship between the two equations. Utilizing these symmetry groups, we derive similarity reductions that yield invariant forms of the equation and facilitate the construction of exact solutions. Finally, we provide certain examples illustrating precise solutions on the related surfaces with positive, negative, and zero Gaussian curvatures, demonstrating the versatility of the approach. This work contributes to the understanding of biharmonic heat equations on symmetric surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00672 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lie point symmetries of the biharmonic heat equation on surfaces of revolution Nass, Aminu Ma'aruf Mpungu, Kassimu Nuruddeen, Rahmatullah Ibrahim Analysis of PDEs Differential Geometry 31A30, 35B06, 58J70 This paper uses Lie symmetry analysis to investigate the biharmonic heat equation on a generalized surface of revolution. We classify the Lie point symmetries associated with this equation, allowing for the identification of surfaces and the corresponding infinitesimal generators. In a significant move, we demonstrate that the biharmonic heat equation on a surface of revolution admits the same Lie symmetries as the harmonic heat equation on the same surface, highlighting a profound structural relationship between the two equations. Utilizing these symmetry groups, we derive similarity reductions that yield invariant forms of the equation and facilitate the construction of exact solutions. Finally, we provide certain examples illustrating precise solutions on the related surfaces with positive, negative, and zero Gaussian curvatures, demonstrating the versatility of the approach. This work contributes to the understanding of biharmonic heat equations on symmetric surfaces. |
| title | Lie point symmetries of the biharmonic heat equation on surfaces of revolution |
| topic | Analysis of PDEs Differential Geometry 31A30, 35B06, 58J70 |
| url | https://arxiv.org/abs/2506.00672 |