메뉴 건너뛰기




Volumn 171, Issue 2, 2001, Pages 251-293

On the initial-boundary value problem for the bipolar hydrodynamic model for semiconductors

Author keywords

Bipolar hydrodynamic model; Compensated compactness; Trace of weak solutions; Zero relaxation limits

Indexed keywords


EID: 0035836936     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2000.3850     Document Type: Article
Times cited : (12)

References (53)
  • 1
    • 0030537690 scopus 로고    scopus 로고
    • On a hierarchy of macroscopic models for semiconductors
    • Ben Abdallah N., Degond P. On a hierarchy of macroscopic models for semiconductors. J. Math. Phys. 37:1996;3306-3333.
    • (1996) J. Math. Phys. , vol.37 , pp. 3306-3333
    • Ben Abdallah, N.1    Degond, P.2
  • 2
    • 0030186891 scopus 로고    scopus 로고
    • An energy-transport model for semiconductors derived from the Boltzmann equation
    • Ben Abdallah N., Degond P., Genieys S. An energy-transport model for semiconductors derived from the Boltzmann equation. J. Statist. Phys. 84:1996;205-231.
    • (1996) J. Statist. Phys. , vol.84 , pp. 205-231
    • Ben Abdallah, N.1    Degond, P.2    Genieys, S.3
  • 3
    • 0014705867 scopus 로고
    • Transport equations for electrons in two-valley semiconductors
    • Blotekjer K. Transport equations for electrons in two-valley semiconductors. IEEE Trans. Electron. Devices. 17:1970;38-47.
    • (1970) IEEE Trans. Electron. Devices , vol.17 , pp. 38-47
    • Blotekjer, K.1
  • 4
    • 0001929964 scopus 로고
    • Convergence of Lax-Friedrichs scheme for isentropic gas dynamics, III
    • Chen G.-Q. Convergence of Lax-Friedrichs scheme for isentropic gas dynamics, III. Acta Math. Sci. 6:1986;75-120.
    • (1986) Acta Math. Sci. , vol.6 , pp. 75-120
    • Chen, G.-Q.1
  • 5
    • 0001895335 scopus 로고
    • Global solutions to the isothermal Euler-Poisson plasma model
    • Cordier S. Global solutions to the isothermal Euler-Poisson plasma model. Appl. Math. Lett. 8:1994;19-24.
    • (1994) Appl. Math. Lett. , vol.8 , pp. 19-24
    • Cordier, S.1
  • 6
    • 0002209968 scopus 로고
    • On a one-dimensional steady-state hydrodynamic model for semiconductors
    • Degond P., Markowich P. A. On a one-dimensional steady-state hydrodynamic model for semiconductors. Appl. Math. Lett. 3:1990;25-29.
    • (1990) Appl. Math. Lett. , vol.3 , pp. 25-29
    • Degond, P.1    Markowich P., A.2
  • 7
    • 0002666718 scopus 로고
    • A steady-state potential model for semiconductors
    • Degond P., Markowich P. A. A steady-state potential model for semiconductors. Ann. Mat. Pura Appl. 4:1993;87-98.
    • (1993) Ann. Mat. Pura Appl. , vol.4 , pp. 87-98
    • Degond, P.1    Markowich P., A.2
  • 8
    • 0032355337 scopus 로고    scopus 로고
    • Macroscopic models for semiconductor heterostructures
    • Degond P., Schmeiser C. Macroscopic models for semiconductor heterostructures. J. Math. Phys. 39:1998;1-30.
    • (1998) J. Math. Phys. , vol.39 , pp. 1-30
    • Degond, P.1    Schmeiser, C.2
  • 10
    • 0000298704 scopus 로고
    • Convergence of the fractional step Lax-Friedrichs scheme for isentropic gas dynamics, I
    • Ding X., Chen G.-Q., Lou P. Convergence of the fractional step Lax-Friedrichs scheme for isentropic gas dynamics, I. Acta Math. Sci. 5:1985;415-432.
    • (1985) Acta Math. Sci. , vol.5 , pp. 415-432
    • Ding, X.1    Chen, G.-Q.2    Lou, P.3
  • 11
    • 0000298704 scopus 로고
    • Convergence of the fractional step Lax-Friedrichs scheme for isentropic gas dynamics, II
    • Ding X., Chen G.-Q., Lou P. Convergence of the fractional step Lax-Friedrichs scheme for isentropic gas dynamics, II. Acta Math. Sci. 5:1985;433-472.
    • (1985) Acta Math. Sci. , vol.5 , pp. 433-472
    • Ding, X.1    Chen, G.-Q.2    Lou, P.3
  • 12
    • 0002337397 scopus 로고
    • Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for isentropic gas dynamics
    • Ding X., Chen G.-Q., Lou P. Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for isentropic gas dynamics. Comm. Math. Phys. 121:1989;63-84.
    • (1989) Comm. Math. Phys. , vol.121 , pp. 63-84
    • Ding, X.1    Chen, G.-Q.2    Lou, P.3
  • 13
    • 0002578353 scopus 로고
    • Convergence of the viscosity method for isentropic gas dynamics
    • DiPerna R. J. Convergence of the viscosity method for isentropic gas dynamics. Comm. Math. Phys. 91:1983;1-30.
    • (1983) Comm. Math. Phys. , vol.91 , pp. 1-30
    • DiPerna R., J.1
  • 14
    • 0020499710 scopus 로고
    • Convergence of approximate solutions to conservation laws
    • DiPerna R. J. Convergence of approximate solutions to conservation laws. Arch. Rational Mech. Anal. 82:1983;27-70.
    • (1983) Arch. Rational Mech. Anal. , vol.82 , pp. 27-70
    • DiPerna R., J.1
  • 15
    • 0031579125 scopus 로고    scopus 로고
    • Steady-state solutions of a one-dimensional hydrodynamic model for semiconductors
    • Fang W., Ito K. Steady-state solutions of a one-dimensional hydrodynamic model for semiconductors. J. Differential Equations. 133:1997;224-244.
    • (1997) J. Differential Equations , vol.133 , pp. 224-244
    • Fang, W.1    Ito, K.2
  • 16
    • 0031103820 scopus 로고    scopus 로고
    • Weak solutions to a one-dimensional hydrodynamic model of semiconductors of two carrier type
    • Fang W., Ito K. Weak solutions to a one-dimensional hydrodynamic model of semiconductors of two carrier type. Nonlinear Anal. 28:1997;947-963.
    • (1997) Nonlinear Anal. , vol.28 , pp. 947-963
    • Fang, W.1    Ito, K.2
  • 17
    • 80053227201 scopus 로고
    • Stationary transonic solutions of a one-dimensional hydrodynamic model for semiconductors
    • Gamba I. M. Stationary transonic solutions of a one-dimensional hydrodynamic model for semiconductors. Comm. Partial Differential Equations. 17:1992;553-577.
    • (1992) Comm. Partial Differential Equations , vol.17 , pp. 553-577
    • Gamba I., M.1
  • 18
    • 84974759770 scopus 로고
    • Limite fluide des équations de Bolzmann des semi-conducteurs pour une statistique de Fermi-Dirac
    • Golse F., Poupaud F. Limite fluide des équations de Bolzmann des semi-conducteurs pour une statistique de Fermi-Dirac. Asymptotic Anal. 6:1992;135-160.
    • (1992) Asymptotic Anal. , vol.6 , pp. 135-160
    • Golse, F.1    Poupaud, F.2
  • 19
    • 21844512215 scopus 로고
    • Global weak solutions to initial boundary value problems for the wave equation with large data
    • Heidrich A. Global weak solutions to initial boundary value problems for the wave equation with large data. Arch. Rational Mech. Anal. 126:1994;333-368.
    • (1994) Arch. Rational Mech. Anal. , vol.126 , pp. 333-368
    • Heidrich, A.1
  • 20
    • 0000262601 scopus 로고    scopus 로고
    • The relaxation of the hydrodynamic model for semiconductors to the drift-diffusion equations
    • Hsiao L., Zhang K. J. The relaxation of the hydrodynamic model for semiconductors to the drift-diffusion equations. J. Differential Equations. 165:2000;315-354.
    • (2000) J. Differential Equations , vol.165 , pp. 315-354
    • Hsiao, L.1    Zhang K., J.2
  • 21
    • 0034368191 scopus 로고    scopus 로고
    • The global weak solution and relaxation limits of the initial-boundary value problem to the bipolar hydrodynamic model for semiconductors
    • Hsiao L., Zhang K. J. The global weak solution and relaxation limits of the initial-boundary value problem to the bipolar hydrodynamic model for semiconductors. Math. Models Methods Appl. Sci. 10:2000;1333-1361.
    • (2000) Math. Models Methods Appl. Sci. , vol.10 , pp. 1333-1361
    • Hsiao, L.1    Zhang K., J.2
  • 22
    • 0022107831 scopus 로고
    • Consistency of semiconductor modelling: An existence/stability analysis for the stationary Van Rroesbrock system
    • Jerome J. W. Consistency of semiconductor modelling: an existence/stability analysis for the stationary Van Rroesbrock system. SIAM J. Appl. Math. 45:1985;565-590.
    • (1985) SIAM J. Appl. Math. , vol.45 , pp. 565-590
    • Jerome J., W.1
  • 23
    • 0000716180 scopus 로고
    • On the existence and uniqueness of transient solutions of a degenerate nonlinear drift-diffusion model for semiconductors
    • Jüngel A. On the existence and uniqueness of transient solutions of a degenerate nonlinear drift-diffusion model for semiconductors. Math. Models Methods Appl. Sci. 4:1994;677-704.
    • (1994) Math. Models Methods Appl. Sci. , vol.4 , pp. 677-704
    • Jüngel, A.1
  • 24
    • 0000637740 scopus 로고
    • Qualitative behaviour of transient solutions of a degenerate nonlinear drift-diffusion model for semiconductors
    • Jüngel A. Qualitative behaviour of transient solutions of a degenerate nonlinear drift-diffusion model for semiconductors. Math. Models Methods Appl. Sci. 5:1995;497-518.
    • (1995) Math. Models Methods Appl. Sci. , vol.5 , pp. 497-518
    • Jüngel, A.1
  • 26
    • 0033475119 scopus 로고    scopus 로고
    • A hierarchy of hydrodanymic models for plasmas: Zero-relaxation-time limits
    • Jüngel A., Peng Y. J. A hierarchy of hydrodanymic models for plasmas: Zero-relaxation-time limits. Comm. Partial Differential Equations. 24:1999;1007-1033.
    • (1999) Comm. Partial Differential Equations , vol.24 , pp. 1007-1033
    • Jüngel, A.1    Peng Y., J.2
  • 27
    • 0003261490 scopus 로고
    • Hyperbolic systems of conservation laws and mathematical theory of shock waves
    • Philadelphia: SIAM
    • Lax P. D. Hyperbolic systems of conservation laws and mathematical theory of shock waves. Regional Conference Series in Applied Mathematics. 1973;SIAM, Philadelphia.
    • (1973) Regional Conference Series in Applied Mathematics
    • Lax P., D.1
  • 29
    • 0003714777 scopus 로고
    • Perturbations singulières dans les problèmes aux limites et en contrôle optimale
    • Berlin: Springer-Verlag
    • Lions J. L. Perturbations singulières dans les problèmes aux limites et en contrôle optimale. Lectures Notes in Math. 1984;Springer-Verlag, Berlin.
    • (1984) Lectures Notes in Math.
    • Lions J., L.1
  • 30
    • 34249763254 scopus 로고
    • Kinetic formulation of the isentropic gas dynamics and p-systems
    • Lions P. L., Perthame B., Tadmor E. Kinetic formulation of the isentropic gas dynamics and p-systems. Comm. Math. Phys. 163:1994;415-431.
    • (1994) Comm. Math. Phys. , vol.163 , pp. 415-431
    • Lions P., L.1    Perthame, B.2    Tadmor, E.3
  • 31
    • 0030539239 scopus 로고    scopus 로고
    • Existence of entropy solutions for the hyperbolic systems of isentroyic gas dynamics in Eulerian and Lagrangian coordinates
    • Lions P. L., Perthame B., Sougandis E. Existence of entropy solutions for the hyperbolic systems of isentroyic gas dynamics in Eulerian and Lagrangian coordinates. Comm. Pure Appl. Math. 44:1996;599-638.
    • (1996) Comm. Pure Appl. Math. , vol.44 , pp. 599-638
    • Lions P., L.1    Perthame, B.2    Sougandis, E.3
  • 32
    • 0000067332 scopus 로고    scopus 로고
    • Large time behavior of the solutions to a hydrodynamic model for semiconductors
    • Lou T., Natalini R., Xin Z. Large time behavior of the solutions to a hydrodynamic model for semiconductors. SIAM J. Math. Anal. 59:1998.
    • (1998) SIAM J. Math. Anal. , vol.59
    • Lou, T.1    Natalini, R.2    Xin, Z.3
  • 33
    • 0000039797 scopus 로고
    • The one-dimensional Darcy's law as the limit of a compressible Euler flow
    • Marcarti P. A., Milani A. The one-dimensional Darcy's law as the limit of a compressible Euler flow. J. Differential Equations. 84:1990;129-147.
    • (1990) J. Differential Equations , vol.84 , pp. 129-147
    • Marcarti P., A.1    Milani, A.2
  • 34
    • 84971109210 scopus 로고
    • Weak solutions to a hydrodynamic model for semiconductors: The Cauchy problem
    • Marcarti P. A., Natalini R. Weak solutions to a hydrodynamic model for semiconductors: The Cauchy problem. Proc. Roy. Soc. Edinburgh Sect. A. 125:1995;115-131.
    • (1995) Proc. Roy. Soc. Edinburgh Sect. A , vol.125 , pp. 115-131
    • Marcarti P., A.1    Natalini, R.2
  • 35
    • 21844490167 scopus 로고
    • Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation
    • Marcarti P. A., Natalini R. Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation. Arch. Rational Mech. Anal. 129:1995;129-145.
    • (1995) Arch. Rational Mech. Anal. , vol.129 , pp. 129-145
    • Marcarti P., A.1    Natalini, R.2
  • 36
    • 0000635085 scopus 로고
    • On steady-state Euler-Poisson model for semiconductors
    • Markowich P. A. On steady-state Euler-Poisson model for semiconductors. Z. Angew. Math. Phys. 62:1991;389-407.
    • (1991) Z. Angew. Math. Phys. , vol.62 , pp. 389-407
    • Markowich P., A.1
  • 38
    • 0021406168 scopus 로고
    • A singular boundary value problem modelling a semiconductor device
    • Markowich P. A., Ringhofer C. A. A singular boundary value problem modelling a semiconductor device. SIAM J. Appl. Math. 44:1984;231-256.
    • (1984) SIAM J. Appl. Math. , vol.44 , pp. 231-256
    • Markowich P., A.1    Ringhofer C., A.2
  • 40
    • 0030584304 scopus 로고    scopus 로고
    • The bipolar hydrodynamic model for semiconductors and the drift-diffusion equation
    • Natalini R. The bipolar hydrodynamic model for semiconductors and the drift-diffusion equation. J. Math. Anal. Appl. 198:1996;262-281.
    • (1996) J. Math. Anal. Appl. , vol.198 , pp. 262-281
    • Natalini, R.1
  • 41
    • 0000110333 scopus 로고
    • Mixed problem for nonlinear conservation laws
    • Nishida T., Smoller J. Mixed problem for nonlinear conservation laws. J. Differential Equations. 23:1977;244-267.
    • (1977) J. Differential Equations , vol.23 , pp. 244-267
    • Nishida, T.1    Smoller, J.2
  • 42
    • 0025545719 scopus 로고
    • On a system of nonlinear Boltzmann equations of semiconductor physics
    • Poupaud F. On a system of nonlinear Boltzmann equations of semiconductor physics. SIAM J. Appl. Math. 50:1990;1593-1606.
    • (1990) SIAM J. Appl. Math. , vol.50 , pp. 1593-1606
    • Poupaud, F.1
  • 43
    • 84974753119 scopus 로고
    • Diffusion approximation of the linear semiconductor Boltzmann equation: Analysis of boundary layers
    • Poupaud F. Diffusion approximation of the linear semiconductor Boltzmann equation: Analysis of boundary layers. Asymptotic Anal. 4:1991;293-317.
    • (1991) Asymptotic Anal. , vol.4 , pp. 293-317
    • Poupaud, F.1
  • 44
    • 58149362452 scopus 로고
    • Global solutions to the isothermal Euler-Poisson system with arbitrary large data
    • Poupaud F., Rascle M., Vila J. P. Global solutions to the isothermal Euler-Poisson system with arbitrary large data. J. Differential Equations. 123:1995;93-121.
    • (1995) J. Differential Equations , vol.123 , pp. 93-121
    • Poupaud, F.1    Rascle, M.2    Vila J., P.3
  • 49
    • 0000440966 scopus 로고
    • Compensated compactness and applications to partial differential equations
    • R. J. Knops. Nonlinear Analysis and Mechanics: Heriot-Watt Symposium. New York: Pitman
    • Tartar L. Compensated compactness and applications to partial differential equations. Knops R. J. Nonlinear Analysis and Mechanics: Heriot-Watt Symposium. Res. Notes Math. 4:1979;136-212 Pitman, New York.
    • (1979) Res. Notes Math. , vol.4 , pp. 136-212
    • Tartar, L.1
  • 50
    • 84944483089 scopus 로고
    • Theory of flow of electrons and holes in germanium and other semiconductors
    • Van Roosbrocck W. V. Theory of flow of electrons and holes in germanium and other semiconductors. Bell System Tech. J. 29:1950;560-607.
    • (1950) Bell System Tech. J. , vol.29 , pp. 560-607
    • Van Roosbrocck W., V.1
  • 51
    • 21344492574 scopus 로고
    • Convergence of the Godunov scheme for a simplified one-dimensional hydrodynamic model for semiconductor devices
    • Zhang B. Convergence of the Godunov scheme for a simplified one-dimensional hydrodynamic model for semiconductor devices. Comm. Math. Phys. 157:1993;1-22.
    • (1993) Comm. Math. Phys. , vol.157 , pp. 1-22
    • Zhang, B.1
  • 52
    • 0000247984 scopus 로고    scopus 로고
    • Global weak solutions of the Cauchy problem to a hydrodynamic model for semiconductors
    • Zhang K. J. Global weak solutions of the Cauchy problem to a hydrodynamic model for semiconductors. J. Partial Differential Equations. 12:1999;369-383.
    • (1999) J. Partial Differential Equations , vol.12 , pp. 369-383
    • Zhang K., J.1
  • 53
    • 0000001766 scopus 로고    scopus 로고
    • Asymptotic behavior of the solution to a nonisentropic hydrodynamic model of semiconductors
    • Zhu Chen, Hattori Harumi. Asymptotic behavior of the solution to a nonisentropic hydrodynamic model of semiconductors. J. Differential Equations. 144:1998;353-389.
    • (1998) J. Differential Equations , vol.144 , pp. 353-389
    • Zhu Chen1    Hattori Harumi2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.