Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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A phase analysis of transonic solutions for the hydrodynamic semiconductor model


Author: Massimiliano D. Rosini
Journal: Quart. Appl. Math. 63 (2005), 251-268
MSC (2000): Primary 82D37; Secondary 35B40, 35L67
DOI: https://doi.org/10.1090/S0033-569X-05-00942-1
Published electronically: February 23, 2005
MathSciNet review: 2150772
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Abstract | References | Similar Articles | Additional Information

Abstract: In the present paper we present a phase plane analysis of transonic solutions of the steady state one-dimensional unipolar hydrodynamic model for semiconductors, taking also into consider shocks.


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  • 1. G. Alì, P. Marcati, R. Natalini, Hydrodynamical models for semiconductors, Z. Angew. Math. Mech., 76, Suppl. 2 1996, pp. 301-304.
  • 2. A. M. Anile, S. Pennisi, Thermodynamic derivation of the hydrodynamical model for charge transport in semiconductors, Physical Review B , Volume 46, Number 20 1992, pp. 186-193.
  • 3. U. M. Asher, P. A. Markowich, P. Pietra, C. Schmeiser, A phase plane analysis of transonic solutions for the hydrodynamic semiconductor model, Math. Models Appl. Sci. 1 1991, pp. 347-376.
  • 4. P. Degond, P. A. Markowich, On a one-dimensional steady-state hydrodynamic model for semiconductors, Appl. Math. Letters 3 (3) 1990, pp. 25-86. MR 1077867 (91m:82155)
  • 5. I. M. Gamba, Stationary transonic solutions for a one-dimensional hydrodynamic model for semiconductors, Comm. Partial Differential Equations 17, no. 3-4 1992, pp. 553-577. MR 1163436 (93f:35186)
  • 6. I. M. Gamba, Boundary-layer formation for viscosity approximations in transonic flow, Phys. Fluids A 4, no. 3 1992, pp. 486-490. MR 1163436 (93f:35186)
  • 7. I. Gasser, R. Natalini, The energy transport and the drift diffusion equations as relaxation limits of the hydrodynamic model for semiconductors, Quart. Appl. Math., 57, no. 2 1999, pp. 269-282. MR 1686190 (2000b:82044)
  • 8. I. Gasser, P. Marcati, The combined relaxation and vanishing Debye length limit in the hydrodynamic model for semiconductor, Math. Methods Appl. Sci., 24, no. 2 2001, pp. 81-92. MR 1808684 (2001k:82112)
  • 9. I. Gasser, P. Marcati, A quasi-neutral limit in the hydrodynamic model for charged fluids, Monatsh. Math., 138, no. 3 2003, pp. 189-208. MR 1969516 (2004b:76158)
  • 10. P. A. Markowich, Kinetic Models for Semiconductors, Nonequilibrium problems in many-particle systems (Montecatini, 1992), Lecture Notes in Math., 1551, Springer, Berlin 1993, pp. 87-111. MR 1296259 (95g:82079)
  • 11. M. D. Rosini, Stability of hydrodynamic model for semiconductor, to appear in Archivum Mathematicum, 2003.
  • 12. M. D. Rosini, Stability of transonic strong shock waves for the one-dimensional hydrodynamic model for semiconductors, Journal of Differential Equations, 199 (2004), pp. 326-351. MR 2047913
  • 13. M. D. Rosini, Existence and Stability of Transonic Shock Waves in the Hydrodynamic Model For Semiconductors, Ph. Thesis Univerity of Naples (Italy), 2003. MR 1707279 (2000g:35142)
  • 14. D. Serre, System of conservation laws, Vol I, Cambridge University Press, Cambridge, 1999.
  • 15. J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer, New York, Heidelberg, Berlin 1983. MR 0688146 (84d:35002)
  • 16. V. I. Tatarskii, The Wigner representation of quantum mechanics, Sov. Phys. Usp. 26 1983, pp. 311-327. MR 0730012 (85k:81061)

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Additional Information

Massimiliano D. Rosini
Affiliation: Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli “Federico II”, Complesso Monte S. Angelo, Via Cintia, 80126 Napoli-Italy
Address at time of publication: Dipartimento di Matematica Pura ed Applicata, Università di L’Aquila, Via Vetoio, 67100 L’Aquila-Italy
Email: mrosini@univaq.it

DOI: https://doi.org/10.1090/S0033-569X-05-00942-1
Keywords: Transonic shock waves, stability, hydrodynamic models, semiconductors
Received by editor(s): April 1, 2003
Published electronically: February 23, 2005
Article copyright: © Copyright 2005 Brown University

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