不定常Kohn-Sham方程的理论研究：新的证明
A theoretical investigation of time-dependent Kohn-Sham equations: new proofs
摘要：
本文给出了一类含时不定常Kohn-Sham方程解的存在性、唯一性和正则性的新分析。Kohn-Sham方程是一个非线性积分型Schroedinger方程，在物理学和计算化学中有着重要的应用。为了处理Kohn-Sham方程的不定常、非线性和非定域势，本文利用能量估计、不动点参数、正则化技术和非定域势项的直接估计等方法进行了分析.考虑的不定常和非线性潜力的假设，使所得到的理论结果也适用于最优控制框架。
英文摘要：
In this paper, a new analysis for existence, uniqueness, and regularity of solutions to a time-dependent Kohn-Sham equation is presented. The Kohn-Sham equation is a nonlinear integral Schroedinger 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.
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