双极非等熵Euler-Poisson方程非常数平衡解的稳定性

Abstract

Abstract:

This article is concerned with the bipolar non-isentropic Euler-Poisson equations in semiconductors. We investigated, by means of an induction argument on the order of the mixed time-space derivatives of solutions in energy estimates and the techniques of symmetrizer, the periodic problem in a three-dimensional torus. Under the assumption that initial data are close to a non constant equilibrium solutions, we prove that the smooth solutions of this problem converge to a steady state with exponential decay rates as the time goes to the infinity. This phenomenon on the charge transport shows the essential difference among the bipolar non-isentropic, the unipolar non-isentropic and the bipolar isentropic Euler-Poisson equations.

Key words: Bipolar non-isentropic Euler-Poisson equations, Semiconductors, Global Smooth Solutions

CLC Number:

O175

Li Xin, Wang Shu, Feng Yuehong. Stability of Non-Constant Equilibrium Solutions for Bipolar Non-Isentropic Euler-Poisson Equations[J].Acta mathematica scientia,Series A, 2016, 36(5): 978-996.

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References

[1] Chen F. Introduction to Plasma Physics and Controlled Fusion. New York: Plenum Press, 1984
[2] Cordier S, Grenier E. Quasineutral limit of an Euler-Poisson system arising from plasma physics. Commun Part Differ Equations, 2000, 23: 1099-1113
[3] Degond P, Markowich P. A steady state potential flow model for semiconductors. Ann Mat Pura Appl, 1993, 52: 87-98
[4] Feng Y H, Peng Y J, Wang S. Stability of non-constant equilibrium solutions for two-fluid Euler-Maxwell systems. Nonlinear Anal Real, 2015, 26: 372-390
[5] Feng Y H, Wang S. Stability of non-constant steady state solutions for non-isentropic Euler-Poisson system in semiconductors. Sci Sin Math, to appear
[6] Guo Y, Strauss W. Stability of semiconductor states with insulating and contact boundary conditions. Arch Rational Mech Anal, 2005, 179: 1-30
[7] Hsiao L, Markowich P, Wang S. The asymptotic behavior of globally smooth solutions of the multidimensional isentropic hydrodynamic model for semiconductors. J Differ Equations, 2003, 192: 111-133
[8] Ju Q C, Li F C, Wang S. Convergence of the Navier-Stokes-Poisson system to the incompressible Navier-Stokes equations. J Math Phys, 2008, 49: 473-515
[9] Jüngel A. Quasi-Hydrodynamic Semiconductor Equations. Paris: Birkhauser, 2001
[10] Kato T. The Cauchy problem for quasi-linear symmetric hyperbolic systems. Arch Rational Mech Anal, 1975, 58: 181-205
[11] Klainerman S, Majda A. Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. Comm Pure Appl Math, 1981, 34: 481-524
[12] Loeper G. Quasi-neutral limit of Euler-Poisson and Euler-Monge-Ampere systems. Commun Part Differ Equations, 2005, 30: 1141-1167
[13] Luo T, Smoller J. Existence and non-linear stability of rotating star solutions of the compressible Euler-Poisson equations. Arch Ration Mech Anal, 2009, 191: 447-496
[14] Majda A. Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables. New York: Springer-Verlag, 1984
[15] Markowich P A, Ringhofer C, Schmeiser C. Semiconductor Equations. New York: Springer, 1990
[16] Matsumura A, Nishida T. The initial value problem for the equation of motion of compressible viscous and heat-conductive fluids. Proc Japan Acad Ser A, 1979, 55: 337-342
[17] Matsumura A, Nishida T. The initial value problem for the equation of motion of viscous and heat-conductive gases. J Math Kyoto Univ, 1980, 20: 67-104
[18] Peng Y J. Stability of steady state solutions for Euler-Maxwell equations. J Math Pures Appl, 2015, 103(1): 39-67
[19] Peng Y J, Wang Y G. Boundary layers and quasi-neutral limit in steady state Euler-Poisson equations for potential flow. Nonlinearity, 2004, 17: 835-849
[20] Peng Y J, Wang Y G. Convergence of compressible Euler-Poisson equations to incompressible type Euler equations. Asymptotic Anal, 2005, 41: 141-160
[21] Peng Y J, Wang Y G, Yong W A. Quasi-neutral limit of the non-isentropic Euler-Poisson system. Proceeding of the Royal Society of Edinburgh: Section A Mathematics, 2006, 136: 1013-1026
[22] Slemrod M, Sternberg N. Quasi-neutral limit for the Euler-Poisson system. J Nonlinear Sci, 2001, 11: 193-209
[23] Rishbeth H, Garriott O K. Introduction to Ionospheric Physics. New York: Academic Press, 1969
[24] Wang S. Quasineutral limit of Euler-Poisson system with and without viscosity. Comm Part Differ Eqs, 2004, 29: 419-456

Stability of Non-Constant Equilibrium Solutions for Bipolar Non-Isentropic Euler-Poisson Equations

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