@article{Ciaramella2021theor-48645,
  year={2021},
  doi={10.1080/00036811.2019.1679792},
  title={A theoretical investigation of time-dependent Kohn–Sham equations : new proofs},
  number={10},
  volume={100},
  issn={0003-6811},
  journal={Applicable Analysis},
  pages={2254--2273},
  author={Ciaramella, Gabriele and Sprengel, Martin and Borzì, Alfio}
}

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    <dcterms:abstract xml:lang="eng">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.</dcterms:abstract>
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    <dc:creator>Borzì, Alfio</dc:creator>
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    <dc:contributor>Sprengel, Martin</dc:contributor>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2020-02-14T12:46:33Z</dc:date>
    <dcterms:title>A theoretical investigation of time-dependent Kohn–Sham equations : new proofs</dcterms:title>
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    <dc:contributor>Borzì, Alfio</dc:contributor>
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