Quantum Euler-Poisson systems: Existence of stationary states

Ansgar Jüngel; Hailiang Li

Archivum Mathematicum (2004)

  • Volume: 040, Issue: 4, page 435-456
  • ISSN: 0044-8753

Abstract

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A one-dimensional quantum Euler-Poisson system for semiconductors for the electron density and the electrostatic potential in bounded intervals is considered. The existence and uniqueness of strong solutions with positive electron density is shown for quite general (possibly non-convex or non-monotone) pressure-density functions under a “subsonic” condition, i.e. assuming sufficiently small current densities. The proof is based on a reformulation of the dispersive third-order equation for the electron density as a nonlinear elliptic fourth-order equation using an exponential transformation of variables.

How to cite

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Jüngel, Ansgar, and Li, Hailiang. "Quantum Euler-Poisson systems: Existence of stationary states." Archivum Mathematicum 040.4 (2004): 435-456. <http://eudml.org/doc/249313>.

@article{Jüngel2004,
abstract = {A one-dimensional quantum Euler-Poisson system for semiconductors for the electron density and the electrostatic potential in bounded intervals is considered. The existence and uniqueness of strong solutions with positive electron density is shown for quite general (possibly non-convex or non-monotone) pressure-density functions under a “subsonic” condition, i.e. assuming sufficiently small current densities. The proof is based on a reformulation of the dispersive third-order equation for the electron density as a nonlinear elliptic fourth-order equation using an exponential transformation of variables.},
author = {Jüngel, Ansgar, Li, Hailiang},
journal = {Archivum Mathematicum},
keywords = {quantum hydrodynamics; existence and uniqueness of solutions; non-monotone pressure; semiconductors; quantum hydrodynamics; existence and uniqueness of solutions; non-monotone pressure; semiconductors},
language = {eng},
number = {4},
pages = {435-456},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Quantum Euler-Poisson systems: Existence of stationary states},
url = {http://eudml.org/doc/249313},
volume = {040},
year = {2004},
}

TY - JOUR
AU - Jüngel, Ansgar
AU - Li, Hailiang
TI - Quantum Euler-Poisson systems: Existence of stationary states
JO - Archivum Mathematicum
PY - 2004
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 040
IS - 4
SP - 435
EP - 456
AB - A one-dimensional quantum Euler-Poisson system for semiconductors for the electron density and the electrostatic potential in bounded intervals is considered. The existence and uniqueness of strong solutions with positive electron density is shown for quite general (possibly non-convex or non-monotone) pressure-density functions under a “subsonic” condition, i.e. assuming sufficiently small current densities. The proof is based on a reformulation of the dispersive third-order equation for the electron density as a nonlinear elliptic fourth-order equation using an exponential transformation of variables.
LA - eng
KW - quantum hydrodynamics; existence and uniqueness of solutions; non-monotone pressure; semiconductors; quantum hydrodynamics; existence and uniqueness of solutions; non-monotone pressure; semiconductors
UR - http://eudml.org/doc/249313
ER -

References

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