Long-time self-similar asymptotic of the macroscopic quantum models

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dc.creatorLi, Hai-Liang
dc.creatorZhang, Guo-Jing
dc.creatorZhang, Min
dc.creatorHao, Chengchun
dc.date2008-11-24
dc.date.accessioned2026-07-07T10:20:36Z
dc.date.available2026-07-07T10:20:36Z
dc.descriptionThe 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.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/0811.3786
dc.identifierhttp://arxiv.org/abs/0811.3786
dc.identifierJ. Math. Phys., 49(07), 073503, 14pp, 2008
dc.identifierdoi:10.1063/1.2949082
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/174898
dc.subjectMathematical Physics
dc.titleLong-time self-similar asymptotic of the macroscopic quantum models
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