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The existence, uniqueness and exponential decay of global solutions in the full quantum hydrodynamic equations for semiconductors

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Abstract

In this paper, we are concerned with the large-time behavior of the solutions in the full quantum hydrodynamic model, which can be used to analyze the thermal and quantum influences on the transport of carriers (electrons or holes) in semiconductor device. For the Cauchy problem in \({\mathbb {R}}^3\), the global existence and uniqueness of smooth solutions, when the initial data are small perturbations of an equilibrium state, are obtained. Also, the solutions tend to the corresponding equilibrium state exponentially fast as the time tends to infinity. The analysis is based on the elementary \(L^2\)-energy method, but various techniques are introduced to establish a priori estimates.

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Authors and Affiliations

  1. Department of Mathematics, University of Science, Pyongyang, Democratic People’s Republic of Korea

    Sungjin Ra

  2. Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People’s Republic of Korea

    Hakho Hong

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  1. Sungjin Ra
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  2. Hakho Hong
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Correspondence to Hakho Hong.

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Ra, S., Hong, H. The existence, uniqueness and exponential decay of global solutions in the full quantum hydrodynamic equations for semiconductors. Z. Angew. Math. Phys. 72, 107 (2021). https://doi.org/10.1007/s00033-021-01540-8

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  • DOI: https://doi.org/10.1007/s00033-021-01540-8

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