Anna Maria Fadda
Existence and convexity of solutions of the fractional heat equation
GRECO, ANTONIO;IANNIZZOTTO, ANTONIO
2017-01-01
Abstract
We prove that the initial-value problem for the fractional heat equation admits an entire solution provided that the (possibly unbounded) initial datum has a conveniently moderate growth at infinity. Under the same growth condition we also prove that the solution is unique. The result does not require any sign assumption, thus complementing the Widder’s type theorem of Barrios et al. [1] for positive solutions. Finally, we show that the fractional heat flow preserves convexity of the initial datum. Incidentally, several properties of stationary convex solutions are established.File | Size | Format | |
---|---|---|---|
Greco-Iannizzotto CPAA.pdf Solo gestori archivio
Type: versione editoriale
Size 520.75 kB
Format Adobe PDF
|
520.75 kB | Adobe PDF | & nbsp; View / Open Request a copy |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.