Potentials for solenoidal fields using the three-dimensional $\varphi$-harmonic cyclic algebra
UDC 517.5 Given a PDE, in [E. López-González, E. A. Martínez-García, R.~Torres-Córdoba, Chaos, Solitons and Fractals, 73, Article 113757 (2023)], the authors proposed a method for the construction of solutions by considering an associative real algebra $\mathbb A$ and a suitable affine vector field...
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| Datum: | 2025 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2025
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7982 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.5
Given a PDE, in [E. López-González, E. A. Martínez-García, R.~Torres-Córdoba, Chaos, Solitons and Fractals, 73, Article 113757 (2023)], the authors proposed a method for the construction of solutions by considering an associative real algebra $\mathbb A$ and a suitable affine vector field $\varphi$ with respect to which the components of all functions $\mathcal L\circ\varphi$ are solutions, where $\mathcal L$ is differentiable in a sense of Lorch with respect to $\mathbb A.$ If we consider the 3D cyclic algebra and a suitable 3D affine map $\varphi,$ then we get families of solutions for the Laplace equation with three independent variables. |
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| DOI: | 10.3842/umzh.v76i11.7982 |