%0 Journal Article
%T 半耗散格点Schrödinger方程组的统计解与Liouville型定理
Statistical Solutions of the Semi-Dissipative Lattice Schrödinger System of Equations and Liouville-Type Theorem
%A 何乐乐
%A 赵才地
%J Advances in Applied Mathematics
%P 450-464
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/aam.2025.145274
%X 本文研究了半耗散格点非线性Schrödinger方程组解的拉回渐近行为及其概率分布。该方程组描述带有杂质的Bose-Einstein浓缩模型,模型中的Bose波函数具有耗散性,杂质波函数的能量守恒。作者首先证明该问题的整体适定性,然后研究Bose波函数在适当意义下拉回吸引子的存在性,接着应用该拉回吸引子和广义Banach极限构造统计解,并证明统计解满足Liouville型定理。
In this paper, the pullback asymptotic behavior of solutions to the nonlinear Schrödinger system of equations with semi-dissipative lattices and their probability distributions are studied. The equations describe the Bose-Einstein condensation model with impurities, in which the Bose wave function is dissipative, and the energy of the impurity wave function is conserved. The authors first prove the global well-posed of the problem and then investigate the existence of a pullback attractor for the Bose wave function in a suitable sense. The authors then apply the pullback attractor and the generalized Banach limit to construct a statistical solution and show that the statistical solution satisfies the Liouville-type theorem.
%K 半耗散格点非线性Schrö
%K dinger方程组,
%K 拉回吸引子,
%K 统计解,
%K Liouville定理
Semi-Dissipative Lattice Nonlinear Schrö
%K dinger System of Equations
%K Pullback Attractor
%K Statistical Solution
%K Liouville Theorem
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=115986