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Keywords:
transonic shock waves; stability; hydrodynamic models; semiconductors
transonic shock waves; stability; hydrodynamic models; semiconductors
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.
References:
[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
[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
[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
[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. MR 1779253 | Zbl 0974.35123
[5] Coifman R. R., Meyer Y.: Au delá des opérateurs pseudo-différentiels. Astérisque 57, 1978, 185 pp. MR 0518170 | Zbl 0483.35082
[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. MR 0678605 | Zbl 0487.35002
[7] Godlewski E., Raviart P. A.: Numerical approximation of hyperbolic systems of conservation laws. Applied Mathematical Sciences 118, New York-Springer 1996. MR 1410987 | Zbl 0860.65075
[8] Kreiss H. O.: Initial boundary value problems for hyperbolic systems. Comm. Pure Appl. Math. XXIII (1970), 277–288. MR 0437941 | Zbl 0215.16801
[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
[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
[11] Majda A.: The stability of multi-dimensional shock fronts. Mem. Amer. Math. Soc. 275 (1983), 95p. Zbl 0506.76075
[12] Majda A.: The existence of multidimensional shocks. Mem. Amer. Math. Soc. 281 (1983), 92p. MR 0699241
[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. MR 0748308 | Zbl 0537.76001
[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.
[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. MR 1328473 | Zbl 0829.35128
[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
[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
[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
[19] Meyer Y.: Remarques sur un théorème de J. M. Bony. Rend. Circ. Mat. Palermo, Suppl., Serie II. 1 (1981), 1–20. MR 0639462 | Zbl 0473.35021
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