Abstract
In this paper, the asymptotic behavior of the global smooth solutions to the Cauchy problem for the one-dimensional nonisentropic Euler-Poisson (or full hydrodynamic) model for semiconductors, where the energy equation with non-zero thermal conductivity coefficient are contained, is discussed. The global existence of smooth solutions for the Cauchy problem with small perturbed initial data is proved. In particular, that the solutions converge to the corresponding stationary solutions exponentially fast as t → ∞ is showed.
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References
Jüngel A. Quasi-Hydrodynamic Semiconductor Equations [M]. Birhuser: Springer-Verlag, 2001.
Markowich P A, Ringhofev C A, Schmeiser C. Semiconductor Equations [M]. New York: Springer-Verlag, 1990.
Luo T, Natalini R, Xin Z. Large Time Behavior of the Solutions to a Hydrodynamic Model for Semiconductors [J]. SIAM J Appl Math, 1998, 59(3): 810–830.
Hsiao L, Wang S. Asymptotic Behavior of Global Smooth Solution to the Full 1D Hydrodynamic Model for Semiconductors [J]. Math Model Meth Appl Sci, 2002, 12: 777–796.
Ali G, Bini D, Rionero S. Global Existence and Relaxation Limit for Smooth Solutions to the Euler-Poisson Model for Semiconductors [J]. SIAM J Math Anal, 2000, 32(3): 572–587.
Hsiao L, Jiang S, Zhang P. On the Global Existence of Smooth Solutions to a Hydrodynamic Model to Semiconductors [J]. Monatsh Math, 2002, 136: 269–285.
Hsiao L, Yang T. Asymptotics of Initial Boundary Value Problems for Hydrodynamic and Drift Diffusion Models for Semiconductors [J]. J Differential Equations, 2001, 170: 472–493.
Li Yeping. The Cauchy-Neumann Problem for a Multidimensional Nonisentropic Hydrodynamic Semiconductor Model [J]. Nonlinearity, 2005, 18: 959–980.
Yeh L. Subsonic Solutions of Hydrodynamic Model for Semiconductors [J]. Math Methods Appl Sci, 1997, 20: 1389–1410.
Zhu C, Hattori H. Asymptotic Behavior of the Solution to a Non-Isentropic Hydrodynamic Model of Semiconductors [J]. J Differential Equations, 1998, 144: 353–389.
Majda A. Compressible Fluid Flow and Systems of Conservation Laws in Serval Space Variables [M]. New York: Springer-Verlag, 1984.
Matsumura A, Nishida T. The Initial Value Problem for the Equations of Motion of Viscous and Heat-Conductive Gases [J]. J Math Kyoto Univ, 1980, 20: 67–104.
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Foundation item: Supported by the Youngth Program of Hubei Provincial Department of Education (Q200628002) and the Innovation Program of Shanghai Municipal Education Commission (08YZ72)
Biography: LI Yeping(1972–), male, Associate professor, Ph.D., research direction: nonlinear partial differential equations.
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Li, Y. Asymptotic behavior of the solutions to the one-dimensional nonisentropic hydrodynamic model for semiconductors. Wuhan Univ. J. Nat. Sci. 13, 141–147 (2008). https://doi.org/10.1007/s11859-008-0204-3
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DOI: https://doi.org/10.1007/s11859-008-0204-3