On the inhomogeneous system of isentropic gas dynamics by the viscosity method

Royal Society of Edinburgh - Proceedings A

Volumn 127, Issue 2, 1997, Pages 261-280

  Fang, Weifu ^a   Ito, Kazufumi ^b  

^a WEST VIRGINIA UNIVERSITY   (United States)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21744434125     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500023647     Document Type: Article

References (16)

1. G.-Q. Chen. Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics (III). Acta Math. Sci. 6 (1986), 75-120.
2. K. Chueh, C. Conley and J. Smoller. Positive invariant regions for systems of nonlinear diffusion equations. Indiana Univ. Math. J. 26 (1979), 373-92.
3. X. Ding, G.-Q. Chen and P. Luo. Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for isentropic gas dynamics. Comm. Math. Phys. 121 (1989), 63-84.
4. R. J. DiPerna. Convergence of approximate solutions to conservation laws. Arch. Rational Mech. Anal. 82 (1983), 27-70.
5. R. J. DiPerna. Convergence of the viscosity method for isentropic gas dynamics. Comm. Math. Phys. 91 (1983), 1-30.
6. L. C. Evans. Weak Convergence Methods for Nonlinear Partial Differential Equations (Providence, RI: American Mathematical Society, 1990).
7. W. Fang and K. Ito. Global solutions of the time-dependent drift-diffusion semiconductor equations. J. Differential Equations 123 (1995), 523-66.
8. W. Fang and K. Ito. One-dimensional hydrodynamic model for semiconductors by viscosity method. In Differential Equations and Applications to Biology and to Industry, 91-9, M. Martelli, K. Cooke, E. Cumberbatch, B. Tang and H. Thieme, eds., (World Scientific, 1996).
9. W. Fang and K. Ito. Weak solutions to a hydrodynamic model of two carrier types for semiconductors. Nonlinear Anal. 28 (1997), 947-63.
10. O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Uralceva. Linear and Quasilinear Equations of Parabolic Type (Providence, RI: American Mathematical Society, 1968).
11. P. Marcati and R. Natalini. Weak solutions to a hydrodynamic model for semiconductors: Cauchy problem. Proc. Roy. Soc. Edinburgh Sect. A 125 (1995), 115-31.
12. P. A. Markowich, C. A. Ringhofer and C. Schmeiser. Semiconductor Equations (New York: Springer, 1990).
13. J. Smoller. Shock Waves and Reaction-Diffusion Equations (New York: Springer, 1983).
14. L. Tartar. Compensated compactness and applications to partial differential equations. Heriot Watt Symposium, Vol. IV (London: Pitman, 1979).
15. G. M. Troianiello. Elliptic Differential Equations and Obstacle Problems (New York: Plenum Press, 1987).
16. B. Zhang. Convergence of the Godunov scheme for a simplified one-dimensional hydrodynamic model for semiconductor devices. Comm. Math. Phys. 157 (1993), 1-22.