A theoretical investigation of time-dependent Kohn–Sham equations: new proofs. Issue 10 (27th July 2021)

• Record Type: Journal Article
• Authors: Ciaramella, G.; Sprengel, M.; Borzi, A.
• Is Part Of: Applicable analysis. Volume 100:Issue 10(2021)
• Page Start: 2254
• Page End: 2273
• Publication Date: 2021-07-27
• Subjects: Kohn–Sham model -- time-dependent density functional theory -- nonlinear Schrödinger equation; 35K55 -- 81Q99; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1679792
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, a new analysis for the existence, uniqueness, and regularity of solutions to a time-dependent Kohn–Sham equation is presented. The Kohn–Sham equation is a nonlinear integral Schrödinger equation that is of great importance in many applications in physics and computational chemistry. To deal with the time-dependent, nonlinear and non-local potentials of the Kohn–Sham equation, the analysis presented in this manuscript makes use of energy estimates, fixed-point arguments, regularization techniques, and direct estimates of the non-local potential terms. The assumptions considered for the time-dependent and nonlinear potentials make the obtained theoretical results suitable to be used also in an optimal control framework.