Methods and Applications of Analysis

Volume 27 (2020)

Number 1

Two computations concerning the isovectors of the backward heat equation with quadratic potential

Pages: 57 – 64

DOI: https://dx.doi.org/10.4310/MAA.2020.v27.n1.a2

Authors

Mohamad Houda (Laboratoire de Mathématiques Raphaël Salem, Université de Rouen, Saint-Étienne-du-Rouvray, France)

Paul Lescot (Laboratoire de Mathématiques Raphaël Salem, Université de Rouen, Saint-Étienne-du-Rouvray, France)

Abstract

We determine the isovectors of the backward heat equation with quadratic potential term in the space variable. This generalizes the calculations of Lescot–Zambrini (cf.[4]). These results first appeared in the first author’s PhD thesis (Rouen, 2013).

Keywords

Lie algebra of isovectors, vector fields, quadratic potential, backward heat equation and Schrödinger equation

2010 Mathematics Subject Classification

17B66, 35B06

Full Text (PDF format)

Received 2 December 2018

Accepted 15 November 2019

Published 12 August 2020