Previous |  Up |  Next

Article

Title: Stability of hydrodynamic model for semiconductor (English)
Author: Rosini, Massimiliano Daniele
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 41
Issue: 1
Year: 2005
Pages: 37-58
Summary lang: English
.
Category: math
.
Summary: In this paper we study the stability of transonic strong shock solutions of the steady state one-dimensional unipolar hydrodynamic model for semiconductors in the isentropic case. The approach is based on the construction of a pseudo-local symmetrizer and on the paradifferential calculus with parameters, which combines the work of Bony-Meyer and the introduction of a large parameter. (English)
Keyword: transonic shock waves
Keyword: stability
Keyword: hydrodynamic models
Keyword: semiconductors
MSC: 35B35
MSC: 35L50
MSC: 35L60
MSC: 35L67
MSC: 35S50
MSC: 76H05
MSC: 76X05
MSC: 82D37
idZBL: Zbl 1112.35020
idMR: MR2142142
.
Date available: 2008-06-06T22:45:05Z
Last updated: 2012-05-10
Stable URL: http://hdl.handle.net/10338.dmlcz/107934
.
Reference: [1] Asher U. M., Markowich P. A., Pietra P., Schmeiser C.: A phase plane analysis of transonic solutions for the hydrodynamic semiconductor model.Math. Models Appl. Sci. 1 (1991), 347–376. MR 1127572
Reference: [2] Bony J. M.: Calcul symbolique et propagation des singularités pour les équations aux dérivées partialles non linéaires.Ann. Sci. Ec. Norm. Sup. Paris 14 (1981), 209–246. MR 0631751
Reference: [3] Bony J. M.: Analyse microlocale des équations aux dérivées partialles non linéaries.Microlocal Analysis and Applications, Montecatini Terme, Lecture Notes in Mathematics 1495 (1989), 1–45. MR 2003416
Reference: [4] Chen Z., Harumi H.: Stability of steady state solutions for an isentropic hydrodynamic model of semiconductors of two species.J. Differential Equations 166 no. 1 (2000), 1–32. Zbl 0974.35123, MR 1779253
Reference: [5] Coifman R. R., Meyer Y.: Au delá des opérateurs pseudo-différentiels.Astérisque 57, 1978, 185 pp. Zbl 0483.35082, MR 0518170
Reference: [6] Chazarain J., Piriou A.: Introduction to the theory of linear partial differential equations.Studies in Mathematics and Its Applications, Vol. 14, Amsterdam-New York-Oxford, 1982. Zbl 0487.35002, MR 0678605
Reference: [7] Godlewski E., Raviart P. A.: Numerical approximation of hyperbolic systems of conservation laws.Applied Mathematical Sciences 118, New York-Springer 1996. Zbl 0860.65075, MR 1410987
Reference: [8] Kreiss H. O.: Initial boundary value problems for hyperbolic systems.Comm. Pure Appl. Math. XXIII (1970), 277–288. Zbl 0215.16801, MR 0437941
Reference: [9] Li H., Markowich P. A., Mei M.: Asymptotic behavior of solutions of the hydrodynamic model of semiconductors.Proc. Royal Soc. Edinburgh 132A (2000), 359–378. MR 1899826
Reference: [10] Majda A.: Smooth solutions for the equations of compressible on incompressible fluid flow.Lecture Notes in Math., Springer-Verlag 1047 (1982), 75–124. MR 0741195
Reference: [11] Majda A.: The stability of multi-dimensional shock fronts.Mem. Amer. Math. Soc. 275 (1983), 95p. Zbl 0506.76075
Reference: [12] Majda A.: The existence of multidimensional shocks.Mem. Amer. Math. Soc. 281 (1983), 92p. MR 0699241
Reference: [13] Majda A.: Compressible fluid flow and systems of conservation laws in several space variables.Appl. Math. Sci., Springer-Verlag, New York 53 (1984), 159p. Zbl 0537.76001, MR 0748308
Reference: [14] Marcati P., Mei M., (to appear) : Asymptotic convergence to steady-state solutions for solutions of the initial boundary problem to a hydrodynamic model for semiconductors.to appear.
Reference: [15] Marcati P., Natalini R.: Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation.Arch. Rational Mech. Anal. 129, no.2 (1995), 129–145. Zbl 0829.35128, MR 1328473
Reference: [16] Marcati P., Natalini R., (1995) : Weak solutions to a hydrodynamic model for semiconductors: the Cauchy problem.Proc. Roy. Soc. Edinburgh Sect. A 125, no.1 (1995), 115–131. MR 1318626
Reference: [17] Markowich P. A.: Kinetic models for semiconductors.In “Nonequilibrium problems in many-particle systems" (Montecatini, 1992), Lecture Notes in Math., Springer, Berlin 1551 (1993), 87–111. MR 1296259
Reference: [18] Métivier G., (2001) : Stability of multidimensional shocks, Advances in the theory of shock waves.Progr. Nonlinear Differential Equations Appl., Birkhäuser Boston, 47 (2001), 25–103. MR 1842775
Reference: [19] Meyer Y.: Remarques sur un théorème de J. M. Bony.Rend. Circ. Mat. Palermo, Suppl., Serie II. 1 (1981), 1–20. Zbl 0473.35021, MR 0639462
.

Files

Files Size Format View
ArchMathRetro_041-2005-1_5.pdf 326.8Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo