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.
@article{107934,
author = {Massimiliano Daniele Rosini},
title = {Stability of hydrodynamic model for semiconductor},
journal = {Archivum Mathematicum},
volume = {041},
year = {2005},
pages = {37-58},
zbl = {1112.35020},
mrnumber = {2142142},
language = {en},
url = {http://dml.mathdoc.fr/item/107934}
}
Rosini, Massimiliano Daniele. Stability of hydrodynamic model for semiconductor. Archivum Mathematicum, Tome 041 (2005) pp. 37-58. http://gdmltest.u-ga.fr/item/107934/
A phase plane analysis of transonic solutions for the hydrodynamic semiconductor model, Math. Models Appl. Sci. 1 (1991), 347–376. (1991) | MR 1127572
Calcul symbolique et propagation des singularités pour les équations aux dérivées partialles non linéaires, Ann. Sci. Ec. Norm. Sup. Paris 14 (1981), 209–246. (1981) | MR 0631751
Analyse microlocale des équations aux dérivées partialles non linéaries, Microlocal Analysis and Applications, Montecatini Terme, Lecture Notes in Mathematics 1495 (1989), 1–45. (1989) | MR 2003416
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
Au delá des opérateurs pseudo-différentiels, Astérisque 57, 1978, 185 pp. (1978) | MR 0518170 | Zbl 0483.35082
Introduction to the theory of linear partial differential equations, Studies in Mathematics and Its Applications, Vol. 14, Amsterdam-New York-Oxford, 1982. (1982) | MR 0678605 | Zbl 0487.35002
Numerical approximation of hyperbolic systems of conservation laws, Applied Mathematical Sciences 118, New York-Springer 1996. (1996) | MR 1410987 | Zbl 0860.65075
Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math. XXIII (1970), 277–288. (1970) | MR 0437941 | Zbl 0215.16801
Asymptotic behavior of solutions of the hydrodynamic model of semiconductors, Proc. Royal Soc. Edinburgh 132A (2000), 359–378. | MR 1899826
Smooth solutions for the equations of compressible on incompressible fluid flow, Lecture Notes in Math., Springer-Verlag 1047 (1982), 75–124. (1982) | MR 0741195
The stability of multi-dimensional shock fronts, Mem. Amer. Math. Soc. 275 (1983), 95p. (1983) | Zbl 0506.76075
The existence of multidimensional shocks, Mem. Amer. Math. Soc. 281 (1983), 92p. (1983) | MR 0699241
Compressible fluid flow and systems of conservation laws in several space variables, Appl. Math. Sci., Springer-Verlag, New York 53 (1984), 159p. (1984) | MR 0748308 | Zbl 0537.76001
Asymptotic convergence to steady-state solutions for solutions of the initial boundary problem to a hydrodynamic model for semiconductors, to appear.
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. (1995) | MR 1328473 | Zbl 0829.35128
Weak solutions to a hydrodynamic model for semiconductors: the Cauchy problem, Proc. Roy. Soc. Edinburgh Sect. A 125, no.1 (1995), 115–131. (1995) | MR 1318626
Kinetic models for semiconductors, In “Nonequilibrium problems in many-particle systems" (Montecatini, 1992), Lecture Notes in Math., Springer, Berlin 1551 (1993), 87–111. (1992) | MR 1296259
Stability of multidimensional shocks, Advances in the theory of shock waves, Progr. Nonlinear Differential Equations Appl., Birkhäuser Boston, 47 (2001), 25–103. | MR 1842775
Remarques sur un théorème de J. M. Bony, Rend. Circ. Mat. Palermo, Suppl., Serie II. 1 (1981), 1–20. (1981) | MR 0639462 | Zbl 0473.35021