On a family of nonzero solutions to the heat equation ut = △u on ℝn+1 which vanish on an arbitrary n-dimensional hyperplane P ⊂ ℝn+1.
In: International Journal of Mathematics, 2024-04-26, S. 1-29
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Zugriff:
Motivated by the paper Rosenbloom–Widder [A temperature function which vanishes initially, Amer. Math. Mon. 65 (8) (1958) 607–609], we construct a more general family of nonzero solutions to the 1-dimensional heat equation ut = uxx on ℝ2 with zero initial data. These solutions are analytically more manageable than the well-known Tychonoff power series solution. Nonzero solutions to the n-dimensional heat equation ut = △u on ℝn+1 with zero initial data (i.e. vanishing on the hyperplane P : {t = 0}) can be easily obtained as a consequence of the examples on ℝ2. Finally, given an arbitrary hyperplane P ⊂ ℝn+1, we can construct a family of nonzero solutions which vanish on P ⊂ ℝn+1. [ABSTRACT FROM AUTHOR]
Titel: |
On a family of nonzero solutions to the heat equation ut = △u on ℝn+1 which vanish on an arbitrary n-dimensional hyperplane P ⊂ ℝn+1.
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Autor/in / Beteiligte Person: | Tsai, Dong-Ho ; Nien, Chia-Hsing |
Zeitschrift: | International Journal of Mathematics, 2024-04-26, S. 1-29 |
Veröffentlichung: | 2024 |
Medientyp: | academicJournal |
ISSN: | 0129-167X (print) |
DOI: | 10.1142/s0129167x24500307 |
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