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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Initial traces and solvability for a semilinear heat equation on a half space of $\mathbb {R}^N$
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by Kotaro Hisa, Kazuhiro Ishige and Jin Takahashi
Trans. Amer. Math. Soc. 376 (2023), 5731-5773
DOI: https://doi.org/10.1090/tran/8922
Published electronically: May 9, 2023

Abstract:

We show the existence and the uniqueness of initial traces of nonnegative solutions to a semilinear heat equation on a half space of $\mathbb {R}^N$ under the zero Dirichlet boundary condition. Furthermore, we obtain necessary conditions and sufficient conditions on the initial data for the solvability of the corresponding Cauchy–Dirichlet problem. Our necessary conditions and sufficient conditions are sharp and enable us to find optimal singularities of initial data for the solvability of the Cauchy–Dirichlet problem.
References
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Bibliographic Information
  • Kotaro Hisa
  • Affiliation: Mathematical Institute, Tohoku University, 6-3 Aoba, Aramaki, Aoba-ku, Sendai 980-8578, Japan
  • MR Author ID: 1279399
  • Email: kotaro.hisa.d5@tohoku.ac.jp
  • Kazuhiro Ishige
  • Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
  • MR Author ID: 357333
  • Email: ishige@ms.u-tokyo.ac.jp
  • Jin Takahashi
  • Affiliation: Department of Mathematical and Computing Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan
  • MR Author ID: 1083499
  • Email: takahashi@c.titech.ac.jp
  • Received by editor(s): September 16, 2022
  • Received by editor(s) in revised form: January 25, 2023
  • Published electronically: May 9, 2023
  • Additional Notes: The first and second authors were supported in part by JSPS KAKENHI Grant Number JP19H05599. The third author was supported in part by JSPS KAKENHI Grant Numbers JP19K14567 and JP22H01131.
  • © Copyright 2023 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 376 (2023), 5731-5773
  • MSC (2020): Primary 35K58; Secondary 35A01, 35A21, 35K20
  • DOI: https://doi.org/10.1090/tran/8922
  • MathSciNet review: 4630758