A phase analysis of transonic solutions for the hydrodynamic semiconductor model

Rosini, Massimiliano

doi:10.1090/S0033-569X-05-00942-1

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
Full-text PDF Free Access

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.

AMN G. Alì, P. Marcati, R. Natalini, Hydrodynamical models for semiconductors, Z. Angew. Math. Mech., 76, Suppl. 2 1996, pp. 301-304.

AP 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.

AMPS 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.

P. Degond and P. A. Markowich, On a one-dimensional steady-state hydrodynamic model for semiconductors, Appl. Math. Lett. 3 (1990), no. 3, 25–29. MR 1077867, DOI https://doi.org/10.1016/0893-9659%2890%2990130-4
Irene Martínez Gamba, Stationary transonic solutions of a one-dimensional hydrodynamic model for semiconductors, Comm. Partial Differential Equations 17 (1992), no. 3-4, 553–577. MR 1163436, DOI https://doi.org/10.1080/03605309208820853
Irene Martínez Gamba, Stationary transonic solutions of a one-dimensional hydrodynamic model for semiconductors, Comm. Partial Differential Equations 17 (1992), no. 3-4, 553–577. MR 1163436, DOI https://doi.org/10.1080/03605309208820853
Ingenuin Gasser and Roberto Natalini, The energy transport and the drift diffusion equations as relaxation limits of the hydrodynamic model for semiconductors, Quart. Appl. Math. 57 (1999), no. 2, 269–282. MR 1686190, DOI https://doi.org/10.1090/qam/1686190
Ingenuin Gasser and Pierangelo Marcati, The combined relaxation and vanishing Debye length limit in the hydrodynamic model for semiconductors, Math. Methods Appl. Sci. 24 (2001), no. 2, 81–92. MR 1808684, DOI https://doi.org/10.1002/1099-1476%2820010125%2924%3A2%3C81%3A%3AAID-MMA198%3E3.3.CO%3B2-O
Ingenuin Gasser and Pierangelo Marcati, A quasi-neutral limit in the hydrodynamic model for charged fluids, Monatsh. Math. 138 (2003), no. 3, 189–208. MR 1969516, DOI https://doi.org/10.1007/s00605-002-0482-3
Peter A. Markowich, Kinetic models for semiconductors, Nonequilibrium problems in many-particle systems (Montecatini, 1992) Lecture Notes in Math., vol. 1551, Springer, Berlin, 1993, pp. 87–111. MR 1296259, DOI https://doi.org/10.1007/BFb0090930

Rosini2 M. D. Rosini, Stability of hydrodynamic model for semiconductor, to appear in Archivum Mathematicum, 2003.

Massimiliano D. Rosini, Stability of transonic strong shock waves for the one-dimensional hydrodynamic model for semiconductors, J. Differential Equations 199 (2004), no. 2, 326–351. MR 2047913, DOI https://doi.org/10.1016/j.jde.2003.09.009
Denis Serre, Systems of conservation laws. 1, Cambridge University Press, Cambridge, 1999. Hyperbolicity, entropies, shock waves; Translated from the 1996 French original by I. N. Sneddon. MR 1707279

Se2 D. Serre, System of conservation laws, Vol I, Cambridge University Press, Cambridge, 1999.

Joel Smoller, Shock waves and reaction-diffusion equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 258, Springer-Verlag, New York-Berlin, 1983. MR 688146
V. I. Tatarskiĭ, The Wigner representation of quantum mechanics, Uspekhi Fiz. Nauk 139 (1983), no. 4, 587–619 (Russian); English transl., Soviet Phys. Uspekhi 26 (1983), no. 4, 311–327. MR 730012, DOI https://doi.org/10.1070/PU1983v026n04ABEH004345