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The asymptotic behavior of globally smooth solutions of the multidimensional isentropic hydrodynamic model for semiconductors. (English) Zbl 1045.35088
The asymptotic behaviour of globally smooth solutions of the Cauchy problem for the multidimensional isentropic hydrodynamic model for semiconductors is studied. It is proved that smooth close to equilibrium solutions of the problem converge to a stationary solution exponentially fast.

35Q60 PDEs in connection with optics and electromagnetic theory
35B40 Asymptotic behavior of solutions to PDEs
82D37 Statistical mechanical studies of semiconductors
Full Text: DOI
[1] G.Q. Chen, J.W. Jerome, B. Zhang, Existence and the singular relaxation limit for the inviscid hydrodynamic energy model, Modeling and Computation for Applications in Mathematics, Science, and Engineering (Evanston, IL, 1996), 189-215, Numerical Mathematics in Science Computation, Oxford University Press, New York, 1998. · Zbl 0948.76007
[2] Chen, G.Q.; Wang, D., Convergence of shock capturing schemes for the compressible euler – poisson equation, Comm. math. phys., 179, 333-364, (1996) · Zbl 0858.76051
[3] Degond, P.; Markowich, P.A., On a one-dimensional steady-state hydrodynamic model for semiconductors, Appl. math. lett., 3, 25-29, (1990) · Zbl 0736.35129
[4] Degond, P.; Markowich, P.A., A steady-state potential flow model for semiconductors, Ann. mat. pura appl., IV, 87-98, (1993) · Zbl 0808.35150
[5] Engelberg, S.; Liu, H.L.; Tadmor, E., Critical thresholds in euler – poisson equations, Indiana univ. math. J., 50, 109-157, (2001) · Zbl 0989.35110
[6] Gamba, I.M., Stationary transonic solutions of a one-dimensional hydrodynamic model for semiconductor, Comm. partial differential equations, 17, 553-577, (1992) · Zbl 0748.35049
[7] Guo, Y., Smooth irrotational fluids in the large to the euler – poisson system in R3+1, Comm. math. phys., 195, 249-265, (1998) · Zbl 0929.35112
[8] Hsiao, L.; Luo, T., Nonlinear diffusive phenomena of solutions for the system of compressible adiabatic flow through porous media, J. differential equations, 125, 329-365, (1996) · Zbl 0859.76067
[9] Hsiao, L.; Luo, T.; Yang, T., Global BV solutions of compressible Euler equations with spherical symmetry and damping, J. differential equations, 146, 203-225, (1998) · Zbl 0916.35090
[10] Hsiao, L.; Wang, S., The asymptotic behavior of global solutions to the hydrodynamic model with spherical symmetry, Nonlinear anal. TMA, 52, 827-850, (2003) · Zbl 1025.35028
[11] L. Hsiao, S. Wang, The asymptotic behavior of global solutions to the hydrodynamic model in the exterior domain, Acta Math. Scientia, accepted.
[12] Hsiao, L.; Yang, T., Asymptotics of initial boundary value problems for hydrodynamic and drift diffusion models for semiconductors, J. differential equations, 170, 472-493, (2001) · Zbl 0986.35110
[13] Hsiao, L.; Zhang, K.J., The relaxation of the hydrodynamic model for semiconductors to the drift-diffusion equations, J. differential equations, 165, 315-354, (2000) · Zbl 0970.35150
[14] Jerome, J.W.; Shu, C.W., Energy models for one-carrier transport in semiconductor devices, (), 185-207 · Zbl 0946.76516
[15] Kato, T., The Cauchy problem for quasilinear symmetric hyperbolic systems, Arch. rational mech. anal., 58, 181-205, (1975) · Zbl 0343.35056
[16] Luo, T.; Natalini, R.; Xin, Z.P., Large-time behavior of the solutions to a hydrodynamic model for semiconductors, SIAM J. appl. math., 59, 810-830, (1998) · Zbl 0936.35111
[17] Majda, A., Compressible fluid flow and systems of conservation laws in several space variables, (1984), Springer-Verlag Berlin/New York · Zbl 0537.76001
[18] Marcati, P.A.; Natalini, R., Weak solutions to hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation, Arch. rational mech. anal., 129, 129-145, (1995) · Zbl 0829.35128
[19] Markowich, P.A., On steady state eurler – poisson model for semiconductors, Z. angew. math. phys., 62, 389-407, (1991) · Zbl 0755.35138
[20] Markowich, P.A.; Ringhofer, C.; Schmeiser, C., Semiconductors equations, (1990), Springer Vienna, New York
[21] Nirenberg, L., On elliptic partial differential equations, Ann. scuola norm. sup. Pisa CI. sci., 13, 115-162, (1959) · Zbl 0088.07601
[22] Stein, E.M., Singular integrals and differentiability properties of functions, (1970), Princeton University Press Princeton, NJ · Zbl 0207.13501
[23] Zhang, B., Convergence of the Godunov scheme for a simplified one-dimensional hydrodynamic model for semiconductor devices, Comm. math. phys., 157, 1-22, (1993) · Zbl 0785.76053
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