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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the eventual local positivity for polyharmonic heat equations
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by Lucas C. F. Ferreira and Vanderley A. Ferreira Jr. PDF
Proc. Amer. Math. Soc. 147 (2019), 4329-4341 Request permission

Abstract:

In this paper we show the eventual local positivity property for higher-order heat equations (including noninteger order). As a consequence, we give a positive answer for an open problem stated by Barbatis and Gazzola [Contemp. Math. 594 (2013)] for polyharmonic heat equations. Moreover, we obtain some polynomial decay properties of solutions.
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Additional Information
  • Lucas C. F. Ferreira
  • Affiliation: IMECC-Department of Mathematics, University of Campinas, Rua Sérgio Buarque de Holanda, 651, CEP 13083-859, Campinas, SP, Brazil
  • MR Author ID: 795159
  • Email: lcff@ime.unicamp.br
  • Vanderley A. Ferreira Jr.
  • Affiliation: Divisão de Ciências Fundamentais, Instituto Tecnológico de Aeronáutica, Praça Marechal Eduardo Gomes, 50, CEP 12228-900, São José dos Campos, SP, Brazil
  • MR Author ID: 1122319
  • Email: ferreira@ita.br
  • Received by editor(s): August 8, 2018
  • Received by editor(s) in revised form: November 25, 2018, and January 11, 2019
  • Published electronically: June 27, 2019
  • Additional Notes: The first author was partially supported by FAPESP grant #2016/16104-8 and CNPq grant #308024/2015-0, Brazil.
    The second author was supported by FAPESP grant #2016/06209-7, Brazil.
  • Communicated by: Joachim Krieger
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4329-4341
  • MSC (2010): Primary 35K25, 26A33, 35Bxx, 35B50, 35B40, 35B05
  • DOI: https://doi.org/10.1090/proc/14565
  • MathSciNet review: 4002545