Research Article

Scaling and instantaneous blow up

Published in: Quaestiones Mathematicae
Volume 47 , issue sup1 , 2024 , pages: 169–177

DOI: 10.2989/16073606.2023.2287834

Author(s): Gisèle Ruiz Goldstein University of Memphis, USA , Jerome A. Goldstein University of Memphis, USA , İsmail Kömbe Istanbul Commerce University, Türkiye , Abdelaziz Rhandi University of Salerno, Italy

Keywords: 35K05 , 35B44 , 35K15 , 35K65 , Heat equation , inverse square potential , instantaneous blow up

Download full text Get new issue alerts

Abstract

The main result is a simple proof of the Baras-Goldstein (1984) instantaneous blow up result for the heat equation with the inverse square potential. The proof relies heavily, indeed mainly, on scaling. Remarks are also given concerning the case when the underlying space ℝ ^N is replaced by the Heisenberg group ℍ ^N .

« Order boundedness and order continuity properties of positive operator semigroups

Hereditarily projectable Archimedean lattice-ordered groups with unit »