×

Stability of steady state solutions for an isentropic hydrodynamic model of semiconductors of two species. (English) Zbl 0974.35123

A \((1+ 1)\)-dimensional \(4\times 4\)-system of nonlinear first-order evolution equations is considered as a model for the dynamics of electrons and holes in a semiconductor. The nonlinear lower-order term models recombination-generation and a nonlocal term models the influence of the doping profile. The authors are concerned with the question of asymptotic stability of the steady state solution of this system for which the paper gives a positive answer provided the doping profile deviates not too much from zero.

MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
35B35 Stability in context of PDEs
35Q35 PDEs in connection with fluid mechanics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Blatt, F.J., Physics of electric conduction in solids, (1968), McGraw-Hill New York
[2] Chen, G.Q.; Wang, D., Convergence of shock capturing scheme for the compressible euler – poisson equations, Commun. math. phys., 179, 333-364, (1996) · Zbl 0858.76051
[3] Degond, P.; Markowich, P.A., On a one-dimensional steady-state hydrodynamic model for semiconductors, Appl. math. lett., 3, 25-29, (1990) · Zbl 0736.35129
[4] Degond, P.; Markowich, P.A., A steady-state potential flow model for semiconductors, Ann. mat. pura. appl. (IV), 87-98, (1993) · Zbl 0808.35150
[5] Fang, W.; Ito, K., Energy estimates for a one-dimensional hydrodynamic model of semiconductors, Appl. math. lett., 9, 65-70, (1996) · Zbl 0868.76006
[6] Fang, W.; Ito, K., Weak solutions to a one-dimensional hydrodynamic model of two carrier types for semiconductors, Nonlinear anal., 28, 947-963, (1997) · Zbl 0876.35114
[7] Gamba, I.M., Stationary transonic solutions of a one-dimensional hydrodynamic model for semiconductor, Commun. partial differential equations, 17, 553-577, (1992) · Zbl 0748.35049
[8] J. H. Hale, Ordinary Differential Equations, pp. 102-117, Wiley-Interscience, New York.
[9] Hattori, H., Stability and instability of steady state solutions for a hydrodynamic model of semiconductors, Proc. roy. soc. Edinburgh sect. A, 127, 781-796, (1997) · Zbl 0889.35107
[10] Henry, D., Geometric theory of semilinear parabolic equations, Lecture notes in mathematics, 840, (1981), Springer-Verlag Berlin/New York, p. 127-138
[11] Hsiao, L.; Liu, T.P., Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping, Comm. math. phys., 143, 599-605, (1992) · Zbl 0763.35058
[12] Jerome, J.W.; Shu, C.W., Energy models for one-carrier transport in semiconductor devices, (), 185-207 · Zbl 0946.76516
[13] Luo, T.; Natalini, R.; Xin, Z., Large time behavior of the solutions to a hydrodynamic model for semiconductors, SIAM J. appl. math., 59, 810-830, (1999) · Zbl 0936.35111
[14] A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Spaces Variables, pp. 30-45, Springer-Verlag, New York.
[15] Matsumura, A.; Nishida, T., The initial value problem for the equations of motion of viscous and heat-conductive gases, J. math. Kyoto univ., 20, 67-104, (1980) · Zbl 0429.76040
[16] Marcati, P.; Natalini, R., Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation, Arch. rat. mech. anal., 129, 129-145, (1995) · Zbl 0829.35128
[17] Markowich, P.A.; Ringhofer, C.A.; Schmeiser, C., Semiconductor equations, (1990), Springer-Verlag Berlin/New York · Zbl 0765.35001
[18] Natalini, R., The bipolar hydrodynamic model for semiconductors and the drift-diffusion equations, J. math. anal. appl., 198, 262-281, (1996) · Zbl 0889.35109
[19] Zhu, C.; Hattori, H., Asymptotic behavior of solutions to a non-isentropic hydrodynamic model of semiconductors, J. differential equations, 144, 353-389, (1998) · Zbl 0913.35060
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.