On the eventual local positivity for polyharmonic heat equations

Ferreira, Lucas; Ferreira Jr., Vanderley

doi:10.1090/proc/14565

On the eventual local positivity for polyharmonic heat equations
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by Lucas C. F. Ferreira and Vanderley A. Ferreira Jr.

Proc. Amer. Math. Soc. 147 (2019), 4329-4341

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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