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On the eventual local positivity for polyharmonic heat equations


Authors: Lucas C. F. Ferreira and Vanderley A. Ferreira Jr.
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
Published electronically: June 27, 2019
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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
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
Email: ferreira@ita.br

DOI: https://doi.org/10.1090/proc/14565
Keywords: Higher order parabolic equations, fractional Laplacian, qualitative properties of solutions, positivity problems, maximum principles, decay of solutions
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
Article copyright: © Copyright 2019 American Mathematical Society