Global existence and relaxation limit for smooth solutions to the Euler-Poisson model for semiconductors

SIAM Journal on Mathematical Analysis

Volumn 32, Issue 3, 2000, Pages 572-587

  Ali G ^a   Bini, D ^a   Rionero, S ^b  

^a CNR   (Italy)

^b UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

Asymptotic behavior; Euler Poisson; Semiconductors; Smooth solutions

Indexed keywords

EID: 0034353696     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141099355174     Document Type: Article

References (16)

1. G. ALÌ, Asymptotic Fluid Dynamic Models for Semiconductors, Quaderno IAC 25/1995, Roma, 1995.
2. G. ALÌ, P. MARCATI, AND R. NATALINI, Hydrodynamic models for semiconductors, Z. Angew. Math. Mech., 76 supp. 2 (1996), pp. 301-304.
3. A. M. ANILE, An extended thermodynamic framework for the hydrodynamical modeling of semiconductors, in Mathematical Problems in Semiconductor Physics (Rome, 1993), Pitman Res. Notes Math. Ser. 340, P. A. Marcati, P. A. Markowich, and R. Natalini, eds., Longman Harlow, UK, 1995, pp. 3-41.
4. K. BLØTEKJÆR, Transport equations for electrons in two-valley semiconductors, IEEE Trans. Electron. Devices, 17 (1970), pp. 38-47.
5. G. BACCARANI AND M. R. WORDEMAN, An investigation of steady-state velocity overshoot effects in Si and GaAs devices, Solid State Electr., 28 (1985), pp. 407-416.
6. G. Q. CHEN, J. W. JEROME, AND B. ZHANG, Existence and the singular relaxation limit for the inviscid hydrodynamic energy model, in Modelling and Computation for Applications in Mathematics, Science, and Engineering (Evanston, IL, 1996), Numer. Math. Sci. Comput., Oxford University Press, New York, 1998, pp. 189-215.
7. P. DEGOND, S. GENIEYS, AND A. JÜNGEL, A steady-state system in nonequilibrium thermodynamics including thermal and electrical effects, C. R. Acad. Sci. Paris Ser. I Math., 324 (1997), pp. 867-872.
8. C. L. GARDNER, J. W. JEROME, AND D. J. ROSE, Numerical methods for the hydrodynamic device model: Subsonic flow, IEEE Trans. Electron. Devices, 8 (1989), pp. 501-507.
9. I. GASSER AND R. NATALINI, The energy transport and the drift diffusion equations as relaxation limits of the hydrodynamic model for semiconductors, Quart. Appl. Math., 57 (1999), pp. 269-282.
10. H. HATTORI AND D. LI, Global solutions of a high-dimensional system for Korteweg materials, J. Math. Anal. Appl., 198 (1996), pp. 84-97.
11. T. LUO, R. NATALINI, AND Z. XIN, Large time behavior of the solutions to a hydrodynamic model for semiconductors, SIAM J. Appl. Math., 59 (1998), pp. 810-830.
12. A. MAJDA, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Appl. Math. Sci. 53, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1984.
13. P. MARCATI AND R. NATALINI, Weak solutions to a hydrodynamic model for semiconductors: The Cauchy problem, Proc. Roy. Soc. Edinburgh Sect. A, 28 (1995), pp. 115-131.
14. P. MARCATI AND R. NATALINI, Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation, Arch. Rational Mech. Anal., 129 (1995), pp. 129-145.
15. A. MATSUMURA AND T. NISHIDA, The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ., 20 (1980), pp. 67-104.
16. P. A. MARKOWICH, C. A. RINGHOFER, AND C. SCHMEISER, Semiconductor Equations, Springer-Verlag, Wien, New York, 1990.