The asymptotic behavior of globally smooth solutions of the multidimensional isentropic hydrodynamic model for semiconductors

Abstract In this paper we study the asymptotic behavior of globally smooth solutions of the Cauchy problem for the multidimensional isentropic hydrodynamic model for semiconductors in R d . We prove that smooth solutions (close to equilibrium) of the problem converge to a stationary solution exponentially fast as t →+∞.

[1]  Peter A. Markowich,et al.  On steady state Euler-Poisson models for semiconductors , 1991 .

[2]  Bo Zhang,et al.  Existence and the singular relaxation limit for the inviscid hydrodynamic energy model , 1998 .

[3]  Shlomo Engelberg,et al.  Critical Thresholds in Euler-Poisson Equations , 2001, math/0112014.

[4]  J. Cooper.  SINGULAR INTEGRALS AND DIFFERENTIABILITY PROPERTIES OF FUNCTIONS , 1973 .

[5]  Roberto Natalini,et al.  Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation , 1995 .

[6]  C. Schmeiser,et al.  Semiconductor equations , 1990 .

[7]  A. Majda.  Compressible fluid flow and systems of conservation laws in several space variables , 1984 .

[8]  Tosio Kato,et al.  The Cauchy problem for quasi-linear symmetric hyperbolic systems , 1975 .

[9]  Ling Hsiao,et al.  Asymptotics of Initial Boundary Value Problems for Hydrodynamic and Drift Diffusion Models for Semiconductors , 2001 .

[10]  Chi-Wang Shu,et al.  Energy Models for One-Carrier Transport in Semiconductor Devices , 1994 .

[11]  L. Nirenberg,et al.  On elliptic partial differential equations , 1959 .

[12]  L. Hsiao,et al.  The asymptotic behavior of global smooth solutions to the hydrodynamic model for semiconductors with spherical symmetry , 2003 .

[13]  Tong Yang,et al.  Global BV Solutions of Compressible Euler Equations with Spherical Symmetry and Damping , 1998 .

[14]  Ling Hsiao,et al.  Nonlinear Diffusive Phenomena of Solutions for the System of Compressible Adiabatic Flow through Porous Media , 1996 .

[15]  Irene M. Gamba.  Stationary transonic solutions of a one—dimensional hydrodynamic model for semiconductors , 1992 .

[16]  Pierre Degond,et al.  On a one-dimensional steady-state hydrodynamic model , 1990 .

[17]  Zhouping Xin,et al.  Large Time Behavior of the Solutions to a Hydrodynamic Model for Semiconductors , 1998, SIAM J. Appl. Math..

[18]  Kaijun Zhang,et al.  The Relaxation of the Hydrodynamic Model for Semiconductors to the Drift–Diffusion Equations , 2000 .

[19]  Bo Zhang,et al.  Convergence of the Godunov scheme for a simplified one-dimensional hydrodynamic model for semiconductor devices , 1993 .

[20]  Yan Guo,et al.  Smooth Irrotational Flows in the Large to the Euler–Poisson System in R3+1 , 1998 .

[21]  Gui-Qiang G. Chen,et al.  Convergence of shock capturing schemes for the compressible Euler-Poisson equations , 1996 .

[22]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[23]  Pierre Degond,et al.  A steady state potential flow model for semiconductors , 1993 .