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Large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductor devices

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Abstract

We are concerned with the global existence and large time behavior of entropy solutions to the one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler–Poisson equations in a bounded interval. In this paper, we first prove the global existence of entropy solution by vanishing viscosity and compensated compactness framework. In particular, the solutions are uniformly bounded with respect to space and time variables by introducing modified Riemann invariants and the theory of invariant region. Based on the uniform estimates of density, we further show that the entropy solution converges to the corresponding unique stationary solution exponentially in time. No any smallness condition is assumed on the initial data and doping profile. Moreover, the novelty in this paper is about the unform bound with respect to time for the weak solutions of the isentropic Euler–Poisson system.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Feimin Huang & Difan Yuan

  2. Academy of Mathematics and System Sciences, CAS, Beijing, 100190, China

    Feimin Huang & Difan Yuan

  3. Hua Loo-Keng Key Laboratory of Mathematics, AMSS, CAS, Beijing, 100190, China

    Tianhong Li

  4. Department of Mathematics, Shandong Normal University, Jinan, 250014, China

    Huimin Yu

Authors
  1. Feimin Huang
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  2. Tianhong Li
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  3. Huimin Yu
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  4. Difan Yuan
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Correspondence to Difan Yuan.

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Huang, F., Li, T., Yu, H. et al. Large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductor devices. Z. Angew. Math. Phys. 69, 69 (2018). https://doi.org/10.1007/s00033-018-0968-z

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  • DOI: https://doi.org/10.1007/s00033-018-0968-z

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