Title:
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Stability of hydrodynamic model for semiconductor (English) |
Author:
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Rosini, Massimiliano Daniele |
Language:
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English |
Journal:
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Archivum Mathematicum |
ISSN:
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0044-8753 (print) |
ISSN:
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1212-5059 (online) |
Volume:
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41 |
Issue:
|
1 |
Year:
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2005 |
Pages:
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37-58 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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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:
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transonic shock waves |
Keyword:
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stability |
Keyword:
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hydrodynamic models |
Keyword:
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semiconductors |
MSC:
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35B35 |
MSC:
|
35L50 |
MSC:
|
35L60 |
MSC:
|
35L67 |
MSC:
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35S50 |
MSC:
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76H05 |
MSC:
|
76X05 |
MSC:
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82D37 |
idZBL:
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Zbl 1112.35020 |
idMR:
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MR2142142 |
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Date available:
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2008-06-06T22:45:05Z |
Last updated:
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2012-05-10 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/107934 |
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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 |
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