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arXiv · 0811.3786

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

Hai-Liang Li·Guo-Jing Zhang·Min Zhang·Chengchun Hao
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Abstract

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.

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Hai-Liang Li, Guo-Jing Zhang, Min Zhang, Chengchun Hao. 2008-11-24. Long-time self-similar asymptotic of the macroscopic quantum models. https://doi.org/10.1063/1.2949082

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