參考文獻 |
[1] G.-Q. Chen, M. Slemrod, D. Wang, Vanishing viscosity method for transonic flow, Arch. Rational Mech. Anal. 189 (2008), pp. 159-188.
[2] S.W. Chou, J.M. Hong, Y.C. Su, An extension of Glimm′s method to the gas dynamical model of transonic flows, Nonlinearity 26 (2013), pp. 1581-1597.
[3] S.W. Chou, J.M. Hong, Y.C. Su, Global entropy solutions of the general non-linear hyperbolic balance laws with time-evolution flux and source, MathodsAppl. Anal., 19 (2012), pp. 43
[4] S.W. Chou, J.M. Hong, Y.C. Su, The initial-boundary value problem of hyperbolic integro-dierential systems of nonlinear balance laws, Nonlinear Anal. 75 (2012), pp. 5933-5960.
[5] C.M. Dafermos, L. Hsiao, Hyperbolic systems of balance laws with inhomogeneity and dissipation, Indiana Univ. Math. J. 31 (1982), pp. 471-491.
[6] G. Dal Maso, P. LeFloch, F. Murat, Denition and weak stability of nonconservative products, J. Math. Pure Appl. 74 (1995), pp. 483-548.
[7] J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Commun. Pure Appl. Math. 18 (1965), pp. 697-715.
[8] J. B. Goodman, Initial boundary value problems for hyperbolic systems of conservation laws, Thesis (Ph. D.){Stanford University., (1983).
[9] P. Goatin, P.G. LeFloch, The Riemann problem for a class of resonant nonlinear systems of balance laws, Ann. Inst. H. Poincare-Analyse Non-lineaire 21 (2004), pp. 881-902.
[10] J. Groah, J. Smoller, B. Temple, Shock Wave Interactions in General Relativity, Monographs in Mathematics, Springer, Berlin, New York, 2007.
[11] J.M. Hong, An extension of Glimm′s method to inhomogeneous strictly hyperbolic systems of conservation laws by weaker than weak" solutions of the Riemann problem, J. Di. Equ. 222 (2006), pp. 515-549.
[12] J.M. Hong, P.G. LeFloch, A version of Glimm method based on generalized Riemann problems, J. Portugal Math. 64, (2007) pp. 199-236.
[13] J.M. Hong, B. Temple, The generic solution of the Riemann problem in a neighborhood of a point of resonance for systems of nonlinear balance laws, Methods Appl. Anal. 10 (2003), pp. 279-294.
[14] J.M. Hong, B. Temple, A bound on the total variation of the conserved quantities for solutions of a general resonant nonlinear balance law, SIAM J. Appl. Math. 64 (2004), pp. 819-857.
[15] J.M. Hong, Y.-C. Su, Generalized Glimm scheme to the initial-boundary value problem of hyperbolic systems of balance laws, Nonlinear Analysis: Theory, Methods and Applications 72 (2010), pp. 635-650.
[16] E. Isaacson, B. Temple, Nonlinear resonance in systems of conservation laws, SIAM J. Appl. Anal. 52 (1992), pp. 1260-1278.
[17] E. Isaacson, B. Temple, Convergence of the 2 2 Godunov method for a general resonant nonlinear balance law, SIAM J. Appl. Math. 55, No. 3 (1995), pp. 625-640.
[18] P.D. Lax, Hyperbolic system of conservation laws II, Commun. Pure Appl. Math. 10 (1957), pp. 537-566.
[19] P.G. LeFloch, Entropy weak solutions to nonlinear hyperbolic systems under nonconservative form, Commun. Part. Di. Equ. 13 (1988) pp. 669-727.
[20] P.G. LeFloch, Shock waves for nonlinear hyperbolic systems in nonconservative form, Institute for Math. and its Appl., Minneapolis, Preprint 593, 1989.
[21] P.G. LeFloch, T.-P. Liu, Existence theory for nonlinear hyperbolic systems in nonconservative form, Forum Math. 5 (1993), pp. 261-280.
[22] P.G. LeFloch, P.A. Raviart, Asymptotic expansion for the solution of the generalized Riemann problem, Part 1, Ann. Inst. H. Poincare, Nonlinear Analysis 5 (1988) pp. 179-209.
[23] Randall J. LeVeque, Numerical Methods for Conservation Laws, Basel, Birkhauser Verlag, 1992.
[24] T.-P. Liu, Quasilinear hyperbolic systems, Commun. Math. Phys. 68 (1979), pp. 141-172.
[25] T.-P. Liu, Nonlinear stability and instability of transonic flows through a nozzle, Commun. Math. Phys. 83 (1982), pp. 243-260.
[26] T.-P. Liu, Nonlinear resonance for quasilinear hyperbolic equation, J. Math. Phys. 28 (1987), pp. 2593-2602.
[27] M. Luskin and B. Temple, The existence of global weak solution to the nonlinear waterhammer problem, Commun. Pure Appl. Math. 35 (1982), pp. 697-735.
[28] C.S. Morawetz, On a weak solution for a transonic
ow problem, Commun. Pure Appl. Math. 38 (1985), pp. 797-817.
[29] J. Smoller, On the solution of the Riemann problem with general stepdata for an extended class of hyperbolic system, Mich. Math. J. 16, pp. 201-210.
[30] J. Smoller, Shock Waves and Reaction-Diusion Equations, 2nd ed., Springer-Verlag, Berlin, New York, 1994.
[31] B. Temple, Global solution of the Cauchy problem for a class of 22 nonstrictly hyperbolic conservation laws, Adv. Appl. Math. 3 (1982), pp. 335-375.
[32] N. Tsuge, Existence of global solutions for isentropic gas
flow in a divergent nozzle with friction, J. Math. Anal. Appl. 426 (2015), pp. 971-977. |