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Author(s)
Li WANG, School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, China
Lei JIN, School of Environment Science and Engineer, Xiamen University of Technology, Xiamen 361024, China
Abstract
Abstract In this paper, the global, nonvacuum solutions with large amplitude to the initialboundary value problem of the onedimensional compressible NavierStokesPoisson system with viscosity and heat conductivity coefficients are considered. The proof is based on the analysis on the positive lower and upper bounds on the specific volume and the absolute temperature.
Keywords
compressible NavierStokesPoisson system; global, nonvacuum solutions with large amplitude; viscosity and heat conductivity coefficients
Cite this paper
Li WANG,
Lei JIN,
Initialboundary Value Problems to the Onedimensional Compressible NavierStokesPoisson Equations with viscosity and heat conductivity coefficients, SCIREA Journal of Mathematics. Vol.
1
, No.
1
,
2016
, pp.
71

94
.
References
[ 1 ]  Gerebeau, J. F. and Bris, C. L. and Lelievre,T. Mathematical methods for the magnetohydrodynamics of liquid metals. Oxford University Press, Oxford, (2006) 
[ 2 ]  Tan, Z., Yang, T., Zhao H. J. and Zhou, Q. Y. Global solutions to the onedimensional compressible NavierStokesPoisson equations with large data. Society for Industrial and Applied Mathematics, 45(2), 547571(2013) 
[ 3 ]  Okada M. and Kawashima, S. On the equations of onedimensional motion of compressible viscous fluids. J. Math. Kyoto Univ., 1, 55–7123 (1983) 
[ 4 ]  Grad, H. Asymptotic Theory of the Boltzmann Equation II. Rarefied Gas Dynamics. J. A. Laurmann, ed., Vol. 1, Academic Press, New York, 2659 (1963) 
[ 5 ]  Zeldovich, Y. B. and Raizer, Y. P. Physics of Shock Waves and HighTemperature Hydrodynamic Phenomena. Academic Press, New York, (1967) 
[ 6 ]  Dafermos, C. M. and Hsiao, C. M. Global smooth thermomechanical processes in onedimensional nonlinear thermoviscoelasticity. Nonlinear Anal., 6, 435454(1982) 
[ 7 ]  Jenssen, H. K. and Karper, T. K. Onedimensional compressible flow with temperature dependent transport coefficients. SIAM J. Math. Anal., 42, 904930(2010) 
[ 8 ]  Jiang, S. and Racke, R. Evolution Equations in Thermoelasticity. Monographs and surveys in pure and applied mathematics, volume 112, Chapman & Hall/CRC Press, Boca Raton, (2000) 
[ 9 ]  Kawohl, B. Global existence of large solutions to initialboundary value problems for a viscous, heatconducting, onedimensional real gas. J. Differential Equations, 58, 76103(1985) 
[ 10 ]  Kawashima, S. and Nishida, T. Global solutions to the initial value problem for the equations of onedimensional motion of viscous polytrophic gases. J. Math. Kyoto Univ., 21(4), 825837(1981) 
[ 11 ]  Kazhikhow, A. V. and Shelukhin, V. V. Unique global solution with respect to time of initialboundary calue problem for onedimensional equations of a viscous gas. J. Appl. Math. Mech., 41(2), 273282(1977) 
[ 12 ]  Kanel, Y. On a model system of equations of onedimensional gas motion. Differencial’nya Uravnenija, 4, 374380(1968) 
[ 13 ]  Chapman, S. and Colwing, T. G. The Mathematical Theory of Nonuniform Gases. Cambrige Math. Lib., 3rd ed., Cambridge University Press, Cambridge, (1990) 
[ 14 ]  Vincenti, W. G. and Kruger, C. H. Introduction to physical Gas Dynamics. Cambridge Math. Lib., Cambridge University Press, Cambridge, (1975) 
[ 15 ]  Tani, A. On the free boundary value problem for compressible viscous fluid motion. J. Math. Kyoto Univ., 21(4), 839–859) (1981) 
[ 16 ]  Ladyzhenskaya, O. A., Solonnikov, V. A. and Ural’ceva, N. N. Linear and quasiequations of parabolic type. Amer. Math. Sot., Providence, R. I., (1968) 