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A theoretical investigation of time-dependent Kohn-Sham equations: new proofs. (English) Zbl 1479.35769

Summary: 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.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35Q41 Time-dependent Schrödinger equations and Dirac equations
35B65 Smoothness and regularity of solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35K55 Nonlinear parabolic equations
82M36 Computational density functional analysis in statistical mechanics
81Q99 General mathematical topics and methods in quantum theory

Software:

COKOSNUT; OCTOPUS
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Full Text: DOI arXiv

References:

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