宏观量子模型的长时间自相似渐近性
Long-time self-similar asymptotic of the macroscopic quantum models
摘要：
本文在一维全空间中考虑了最近在电荷输运领域导出的单极和双极宏观量子模型。这些模型在单极情况下由非线性四阶抛物型方程组成，在双极情况下由耦合的非线性四阶抛物型方程组组成。首次证明了宏观量子模型在大时间内的自相似性。也就是说，我们证明了宏观量子模型的初值问题存在唯一的具有严格正密度的整体强解，该解在大时间内以代数时间衰减率趋向于自相似波（这不是模型的精确解）.
英文摘要：
The unipolar and bipolar macroscopic quantum models derived recently for instance in the area of charge transport are considered in spatial one-dimensional whole space in the present paper. These models consist of nonlinear fourth-order parabolic equation for unipolar case or coupled nonlinear fourth-order parabolic system for bipolar case. We show for the first time the self-similarity property of the macroscopic quantum models in large time. Namely, we show that there exists a unique global strong solution with strictly positive density to the initial value problem of the macroscopic quantum models which tends to a self-similar wave (which is not the exact solution of the models) in large time at an algebraic time-decay rate.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
