ON THE EVENTUAL LOCAL POSITIVITY FOR POLYHARMONIC HEAT EQUATIONS.

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. [ABSTRACT FROM AUTHOR]