タイトル:
Systems of a Hyperbolic-Parabolic Composite Type, with Applications to the Equations of Magnetohydrodynamics

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121.N. Mori, J. Xu and S. Kawashima, Global existence and optimal decay rares for the Timoshenko system: the case of equal wave speeds, J. Diff. Equations, 258(2015), 1494-1518.

120.S. Kawashima and Y.-Z. Wang, Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation, Analysis and Applications, 13(2015), 233-255.

119.Y.H. Feng, S. Wang and S. Kawashima, Global existence and asymptotic decay of solutions to the non-isentropic Euler-Maxwell system, Math. Models Meth. Appl. Sci, 24(2014), 2851-2884.

118.N. Mori and S. Kawashima, Decay property for the Timoshenko system with Fourier's type heat conduction, J. Hyperbolic Differential Equations, 11(2014), 135-157.

117.J. Xu and S. Kawashima, Diffusive relaxation limit of classical solutions to the damped compressible Euler equations, J. Diff. Equations, 256(2014), 771-796.

116.J. Xu and S. Kawashima, Global classical solutions for partially dissipative hyperbolic systems of balance laws, Arch. Rat. Mech. Anal., 211 (2014), 513-553.

115.M. Kato, Y.-Z. Wang and S. Kawashima, Asymptotic behavior of solutions to the generalized cubic double dispersion equation in one space dimension, Kinetic and Related Models, 6 (2013), 969-987.

114.J. Xu, J. Xiong and S. Kawashima, Global well-posedness in critical Besov spaces for two-fluid Euler-Maxwell equations, SIAM J. Math. Anal., 45 (2013), 1422-1447.

113.Y. Liu and S. Kawashima, Global existence and asymptotic decay of solutions to the nonlinear Timoshenko system with memory, Nonlinear Analysis, TMA, 84 (2013), 1-17.

112.R. Kobayashi, M. Yamamoto and S. Kawashima, Asymptotic stability of stationary solutions to the drift-diffusion model in the whole space, ESAIM: Control, Optimisation and Calculus of Variations, 18 (2012), 1097-1121.

111. Y. Ueda, S. Wang and S. Kawashima, Dissipative structure of the regularity-loss type and time asymptotic decay of solutions for the Euler-Maxwell system, SIAM J. Math. Anal., 44 (2012), 2002-2017.

110.P.M.N. Dharmawardane, T. Nakamura and S. Kawashima, Decay estimates of solutions for quasi-linear hyperbolic systems of viscoelasticity, SIAM J. Math. Anal., 44 (2012), 1976-2001.

109.Y. Ueda, R.-J. Duan and S. Kawashima, Decay structure for symmetric hyperbolic systems with non-symmetric relaxlation and its applications, Arch. Rat. Mech. Anal., 205 (2012), 239-266.

108.Y. Liu and S. Kawashima, Decay property for the Timoshenko system with memory-type dissipation, Math. Models Meth. Appl. Sci., 22 (2012), -

108. S. Kawashima, C.-K. Lin and J.-I. Segata, The initial value problem for some hyperbolic-dispersive system, Math. Meth. Appl. Sci. 35 (2012), 125-133.

107. Y. Ueda and S. Kawashima, Decay property of regularity-loss type for the Euler-Maxwell system, Methods and Applications of Analysis. 18(2011), 245-268.

106. S. Kawashima, Decay structure for systems of viscoelasticity, Proceedings of the International Cenference ”Mathematical Analysis on the Navier-Stokes equations and Related Topics, Past and Future -- in memory of Professor Tetsuro Miyakawa”, Math. Sci. Appl. 35 (2011), 91-102.

105. P.M.N. Dharmawardane, T. Nakamura and S. Kawashima, Time weighted energy method for quasi-linear hyperbolic systems of viscoelasticity, Proc. Japan Acad., 87 (2011), 99-102.

104. Y. Liu and S. Kawashima, Global existence and decay of solutions for a quasi-linear dissipative plate equation, J. Hyperbolic Differential Equations. 8 (2011), 591-614

103. Y. Liu and S. Kawashima, Decay property for a plate equation with memory-type dissipation, Kinetic and Related Models. 4 (2011), 531--547.

102. P.M.N. Dharmawardane, T. Nakamura and S. Kawashima, Global solutions to quasi-linear hyperbolic systems of viscoelasticity, Kyoto J. Math., 51 (2011), 467-483.

101. Y. Ueda, T. Nakamura and S. Kawashima, Energy method in the partial Fourier space and application to stability problems in the half space, J. Diff. Equations, 250 (2011), 1169-1199.

100. Y. Liu and S. Kawashima, Asymptotic behavior of solutions to a model system of a radiating gas, Comm. Pure Appl. Anal., 10 (2011), 209-223.

99. Y. Liu and S. Kawashima, Global existence and asymptotic behavior of solutions for quasi-linear dissipative plate equation, Discrete Continuous Dynamical Systems, A, 29 (2011), 1113-1139.

98. S. Kawashima and P. Zhu, Traveling waves for models of phase transitions of solids driven by configurational forces, Discrete Continuous Dynamical Systems, B, 15 (2011), 309-323.

97.S. Kawashima, T. Nakamura, S. Nishibata and P. Zhu, Stationary waves to viscous heat-conductive gases in half space: Existence, stability and convergencerate, Math. Models Meth. Appl. Sci., 20 (2010), 2201-2235.

96. Y. Ueda, T. Nakamura and S. Kawashima, Convergence rate toward degeneratestationary wave for compressible viscous gases, Proceedings of the InternationalConference on Nonlinear Analysis and Convex Analysis (Tokyo, Japn, 2009), Yokohama Publ., (2010), 239-248.

95. Y. Sugitani and S. Kawashima, Decay estimates of solutions to a semi-linear dissipative plate equation, J. Hyperbolic Differential Equations 7 (2010), 471-501.

94. P.M.N. Dharmawardane, J.M. Rivera and S. Kawashima, Decay property for second order hyperbolic systems of viscoelastic materials, J. Math. Anal. Appl., 360 (2010), 621-635.

93. Y. Ueda, T. Nakamura and S. Kawashima, Stability of degenerate stationary waves for viscous gases, Arch. Rat. Mech. Anal., 198 (2010), 735-763.

92. I. Hashimoto, Y. Ueda and S. Kawashima, Convergence rate to the nonlinear waves for viscous conservation laws on the half line, Methods and Applications of Analysis, 16 (2009), 389-402.

91. H. Hataya and S. Kawashima, Decaying solution of the Navier-Stokes flow of infinite volume without surface tension, Nonlinear Analysis, 71 (2009), 2535-2539.

90. S. Kawashima and M. Kurata, Hardy type inequality and application to the stability of degenerate stationary waves, J. Func. Anal., 257 (2009), 1-19.

89. 川島秀一, 緩和的双曲型保存則系の数学解析, 雑誌「数学」61 巻3 号, (2009 年7 月), 248-269.

88. R. Kobayashi, M. Kurokiba and S. Kawashima, Stationary solutions to the driftdiffusion model in the whole space, Math. Meth. Appl. Sci., 32 (2009), 640-652.

87. Y. Ueda, T. Nakamura and S. Kawashima, Stability of planar stationary waves for damped wave equations with nonlinear convection in half space, Hyperbolic Problems: Theory, Numerics and Applications (E. Tadmor, J.-G. Liu and A. Tzavaras,eds.), Proceedings of Symposia in Applied Mathematics, 67 (2009), 977-986.

86. S. Kawashima and P. Zhu, Asymptotic stability of rarefaction wave for the NavierStokes equations for a compressible fluid in the half space, Arch. Rat. Mech. Anal., 194 (2009), 105-132.

85. T. Kubo and S. Kawashima, Decay property of regularity-loss type and nonlinear effects for some hyperbolic-elliptic system, Kyushu J. Math., 63 (2009), 1-21.

84. S. Kawashima and W.-A. Yong, Decay estimates for hyperbolic balance laws, ZAA, J. Anal. Appl., 28 (2009), 1-33.

83. R. Kobayashi and S. Kawashima, Decay estimates and large time behavior of solutions to the drift-diffusion system, Funkcialaj Ekvacioj, 51 (2008), 371-394.

82. S. Kawashima and P. Zhu, Asymptotic stability of nonlinear wave for the compressible Navier-Stokes equations in the half space, J. Diff. Equations, 244 (2008), 3151-3179.

81. K. Ide and S. Kawashima, Decay property of regularity-loss type and nonlinear effects for dissipative Timoshenko system, Math. Models Meth. Appl. Sci., 18 (2008), 1001-1025.

80. K. Ide, K. Haramoto and S. Kawashima, Decay property of regularity-loss typefor dissipative Timoshenko system, Math. Models Meth. Appl. Sci., 18 (2008), 647-667.

79. Y. Ueda, T. Nakamura and S. Kawashima, Stability of planar stationary waves for damped wave equations with nonlinear convection in multi-dimensional half space, Kinetic and Related Models, 1 (2008), 49-64.

78. S. Kawashima, Dissipative structure of regularity-loss type and applications, Hyperbolic Problems: Theory, Numerics, Applications (S. Benzoni-Gavage, D. Serre, eds.), Springer-Verlag, Berlin, Heidelberg, (2008), 45-57.

77. Y. Ueda and S. Kawashima, Large time behavior of solutions to a semilinear hyperbolic system with relaxation, J. Hyperbolic Differential Equations, 4 (2007), 147-179.

76. T. Hosono and S. Kawashima, Decay property of regularity-loss type and application to some nonlinear hyperbolic-elliptic system, Math. Models Meth. Appl. Sci., 16 (2006), 1839-1859.

75. Y. Kagei and S. Kawashima, Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space, Commun. Math. Phys., 266 (2006), 401-430.

74. Y. Kagei and S. Kawashima, Local solvability of an initial boundary value problem for a quasilinear hyperbolic-parabolic system, J. Hyperbolic Differential Equations, 3 (2006), 195-232.

73. S. Kawashima and W.-A. Yong, Dissipative structure and entropy for hyperbolic systems of balance laws, Arch. Rat. Mech. Anal., 174 (2004), 345-364.

72. S. Kawashima, S. Nishibata and M. Nishikawa, $L^p$ energy method for multi-dimensional viscous conservation laws and application to the stability of planar waves, J. Hyperbolic Differential Equations, 1 (2004), 581-603.

71. S. Kawashima and Y. Tanaka, Stability of rarefaction waves for a model system of a radiating gas, Kyushu J. Math., 58 (2004), 211-250.

70. S. Kawashima, Y. Nikkuni and S. Nishibata, Large-time behavior of solutions to hyperbolic-elliptic coupled systems, Arch. Rat. Mech. Anal., 170 (2003), 297-329.

69. S. Kawashima, S. Nishibata and P. Zhu, Asymptotic stability of the stationary solution to the compressible Navier-Stokes equations in the half space, Commun. Math. Phys., 240 (2003), 483-500.

68. S. Kawashima, S. Nishibata and M. Nishikawa, Asymptotic stability of stationary waves for two-dimensional viscous conservation laws in half plane, Discrete and Continuous Dynamical Systems, Supplement Vol. (2003), 469-476.

67. Y. Nikkuni and S. Kawashima, Asymptotic stability of rarefaction waves for some discrete velocity model of the Boltzmann equation in the half-space, Adv. Math. Sci. Appl., 12 (2002), 327-353.

66. T. Iguchi and S. Kawashima, On space-time decay properties of solutions to hyperbolicelliptic coupled systems, Hiroshima Math. J., 32 (2002), 229-308.

65. S. Kawashima and S. Nishibata, Stationary waves for the discrete Boltzmann equations in the half space, Hyperbolic Problems: Theory, Numerics, Applications (H. Freist$\ddot{u}$hler and G. Warnecke, eds), Birkh$\ddot{a}$user, ISNM Vol. 141, (2001), 593-602.

64. S. Kawashima and S. Nishibata, A singular limit for hyperbolic-elliptic coupled systems in radiation hydrodynamics, Indiana Univ. Math. J., 50 (2001), 567-589.

63. S. Kawashima and S. Nishibata, Stationary waves for the discrete Boltzmann equation in the half space with reflective boundaries, Commun. Math. Phys., 211 (2000), 183-206.

62. Y. Nikkuni and S. Kawashima, Stability of stationary solutions to the half-space problem for the discrete Boltzmann equation with multiple collisions, Kyushu J. Math., 54 (2000), 233-255.

61. S. Kawashima and S. Nishibata, Existence of a stationary wave for the discrete Boltzmann equation in the half space, Commun. Math. Phys., 207 (1999), 385-409.

60. S. Kawashima and S. Nishibata, Cauchy problem for a model system of the radiating gas: Weak solutions with a jump and classical solutions, Math. Models Meth. Appl. Sci., 9 (1999), 69-91.

59. S. Kawashima, Y. Nikkuni and S. Nishibata, The initial value problem for hyperbolicelliptic coupled systems and applications to radiation hydrodynamics, Analysis of Systems of Conservation Laws (H. Freist$\ddot{u}$hler, ed.), Chapman & Hall/CRC, (1998), 87-127.

58. S. Kawashima and S. Nishibata, Weak solutions with a shock for a model system of the radiating gas, Science Bulletin of Josai Univ., Special Issue, 5 (1998), 119-130.

57. S. Kawashima and S. Nishibata, Shock waves for a model system of the radiating gas, SIAM J. Math. Anal., 30 (1998), 95-117.

56. H. Hoshino and S. Kawashima, Exponentially decaying component of a global solution to a reaction-diffusion system, Math. Models Meth. Appl. Sci., 8 (1998), 897-904.

55. S. Kawashima and H. Hattori, Smooth shock profiles in viscoelasticity with memory, Nonlinear Evolutionary Partial Differential Equations (X.-X. Ding and T.-P. Liu, eds), Studies in Advanced Mathematics, 3, AMS International Press, (1997), 271-281.

54. H. Hattori and S. Kawashima, Nonlinear stability of travelling wave solutions for viscoelastic materials with fading memory, J. Diff. Equations, 127 (1996), 174-196.

53. Y. Ebihara, S. Kawashima and H.A. Levine, On solutions to $u_{tt}-|x|^{\alpha}\Delta u = f(u) (\alpha>0)$, Funkcialaj Ekvacioj, 38 (1995), 539-544.

52. H. Hoshino and S. Kawashima, Asymptotic equivalence of a reaction-diffusion system to the corresponding system of ordinary differential equations, Math. Models Meth. Appl. Sci., 5 (1995), 813-834.

51. S. Kawashima, M. Nakao and K. Ono, On the decay property of solutions to theCauchy problem of the semilinear wave equation with a dissipative term, J. Math.Soc. Japan, 47 (1995), 617-653.

50. S. Kawashima and H. Hattori, Existence of shock profiles for viscoelastic materials with memory, SIAM J. Math. Anal., 26 (1995), 1130-1142.

49. S. Kawashima and Y. Shibata, On the Neumann problem of one-dimensional nonlinear thermoelasticity with time-independent external forces, Czechoslovak Math. J., 45 (1995), 39-67.

48. K. Ito and S. Kawashima, Asymptotic behavior of solutions to the Burgers equation with a nonlocal term, Nonlinear Analysis, T.M.A., 23 (1994), 1533-1543.

47. S. Kawashima and A. Matsumura, Stability of shock profiles in viscoelasticity with non-convex constitutive relations, Comm. Pure Appl. Math., 47 (1994), 1547-1569.

46. S. Kawashima, Self-similar solutions of a convection-diffusion equation, Nonlinear PDE-JAPAN Symposium 2 (K. Masuda, M. Mimura and T. Nishida, eds.), Lecture Notes in Num. Appl. Anal., 12, Kinokuniya, (1993), 123-136.

45. S. Kawashima, The discrete Boltzmann equation with multiple collisions and the corresponding fluid-dynamical equations, Math. Models Meth. Appl. Sci., 3 (1993),681-692.

44. S. Kawashima, Global solutions to the equation of viscoelasticity with fading memory, J. Diff. Equations, 101 (1993), 388-420.

43. S. Kawashima, Large-time behavior of solutions to the discrete Boltzmann equation in the half-space, Transport Theor. Stat. Phys., 21 (1992), 451-463.

42. S. Kawashima and Y. Shibata, Global existence and exponential stability of small solutions to nonlinear viscoelasticity, Commun. Math. Phys., 148 (1992), 189-208.

41. S. Kawashima, Exponential stability of stationary solutions to the discrete Boltzmann equation in a bounded domain, Math. Models Meth. Appl. Sci., 2 (1992),239-248.

40. S. Kawashima, Existence and stability of stationary solutions to the discrete Boltzman equation, Japan J. Indust. Appl. Math., 8 (1991), 389-429.

39. S. Kawashima, Global solutions to the initial-boundary value problems for the discrete Boltzmann equation, Nonlinear Analysis, T.M.A., 17 (1991), 577-597.

38. S. Kawashima and N. Bellomo, On the Euler equation in discrete kinetic theory, Advances in Kinetic Theory and Continuum Mechanics (R. Gatignol and Soubbaramayer, eds.), Springer-Verlag, (1991), 73-80.

37. S. Kawashima, Asymptotic behavior of solutions to the discrete Boltzmann equation, Discrete Models of Fluid Dynamics (A.S. Alves, ed.), Series on Advances in Mathematics for Applied Sciences, 2, World Scientific, (1991), 35-44.

36. S. Kawashima and N. Bellomo, The discrete Boltzmann equation with multiple collisions: Global existence and stability for the initial value problem, J. Math. Phys., 31 (1990), 245-253.

35. S. Kawashima, The Boltzmann equation and thirteen moments, Japan J. Appl. Math., 7 (1990), 301-320.

34. S. Kawashima and H. Cabannes, Initial-value problem in discrete kinetic theory, Rarefied Gas Dynamics: Theoretical and Computational Techniques (E.P. Muntz,D.P. Weaver and D.H. Campbell, eds.), Progress in Astronautics and Aeronautics, 118, (1989), 148-154.

33. S. Kawashima, A new approach to the Boltzmann equation, Discrete Kinetic Theory, Lattice Gas Dynamics and Foundation of Hydrodynamics (R. Monaco, ed.), World Scientific, (1989), 192-205.

32. S. Kawashima and Y. Shizuta, The Navier-Stokes equation associated with the discrete Boltzmann equation, Recent Topics in Nonlinear PDE IV (M. Mimura and T. Nishida, eds.), Lecture Notes in Num. Appl. Anal., 10, Kinokuniya, (1989), 15-30.

31. S. Kawashima, Initial-boundary value problem for the discrete Boltzmann equation, Journ$\acute{e}$es $\acute{E}$quations aux D$\acute{e}$riv$\acute{e}$es Partielles, Centre de Math$\acute{e}$matiques, Ecole Polytechnique, (1988).

30. S. Kawashima and Y. Shizuta, The Navier-Stokes equation in the discrete kinetic theory, J. M$\acute{e}$can. th$\acute{e}$or. appl., 7 (1988), 597-621.

29. S. Kawashima and Y. Shizuta, On the normal form of the symmetric hyperbolicparabolic systems associated with the conservation laws, T$\hat{o}$ohoku Math. J., 40 (1988), 449-464.

28.H. Cabannes and S. Kawashima，Le probl$\acute{e}$me aux valeurs initiales en th$\acute{e}$orie cin$\acute{e}$tique discr$\acute{e}$te， C. R. Acad. Sci. Paris，307 (1988)，507-511.

27. T. Makino，S. Ukai and S. Kawashima，On compactly supported solutions of thecompressible Euler equation，Recent Topics in Nonlinear PDE III (K. Masuda and　T. Suzuki，eds.)， Lecture Notes in Num. Appl. Anal., 9，Kinokuniya, (1987)，173-183.

26. S. Kawashima，The Boltzmann equation and thirteen moments，Recent Topics in Nonlinear PDE III (K. Masuda and T. Suzuki，eds.)Lecture Notes in Num. Appl. Anal.，9，Kinokuniya，(1987)，157-172.

25. S. Kawashima，T. Yanagisawa and Y. Shizuta，Mixed problems for quasi-linearsymmetric hyperbolic systems，Proc. Japan Acad.，63 (1987)，243-246.

24. S. Kawashima，Asymptotic stability of Maxwellians of the discrete Boltzmann equation, Transport Theor. Stat. Phys.，16 (1987)，781-793.

23. S. Kawashima，Large-time behavior of solutions of the discrete Boltzmann equation, Commun. Math. Phys.，109 (1987)，563-589.

22. S. Kawashima，Large-time behaviour of solutions to hyperbolic-parabolic systems of conservation laws and applications，Proc. Roy. Soc. Edinburgh，106A (1987), 169-194.

21. Y. Shizuta and S. Kawashima，The regular discrete models of the Boltzmann equation, J. Math. Kyoto Univ.，27 (1987)，131-140.

20. Y. Shizuta，M. Maeji，A. Watanabe and S. Kawashima，The 102-velocity model and the related discrete models of the Boltzmann equation，Proc. Japan Acad.，62 (1986)，367-370.

19. T. Makino，S. Ukai and S. Kawashima，Sur la solution $\acute{a}$ support compact del'equation d'Euler compressible，Japan J. Appl. Math.，3 (1986)，249-257.

18. S. Kawashima，Large-time behavior of solutions for hyperbolic-parabolic systems of conservation laws，Proc. Japan Acad.，62 (1986)，285-287.

17. S. Kawashima，A. Matsumura and K. Nishihara，Asymptotic behavior of solutions for the equations of a viscous heat-conductive gas，Proc. Japan Acad.，62 (1986), 249-252.

16. S. Kawashima，A. Watanabe，M. Maeji and Y. Shizuta，On Cabannes' 32-velocitymodels of the Boltzmann equation，Publ. RIMS，Kyoto Univ.，22 (1986)，583-607.

15. S. Kawashima and Y. Shizuta，Magnetohydrodynamic approximation of the complete equations for an electromagnetic fluid II，Proc. Japan Acad.，62 (1986), 181-184.

14. Y. Shizuta，M. Maeji，A. Watanabe and S. Kawashima，Regularity of the 90-velocity model of the Boltzmann equation，Proc. Japan Acad.，62 (1986)，171-173.

13. S. Kawashima and Y. Shizuta，Magnetohydrodynamic approximation of the complete equations for an electromagnetic fluid，Tsukuba J. Math.，10 (1986)，131-149.

12. Y. Shizutaand S. Kawashima，The regularity of discrete models of the Boltzmann equation， Proc. Japan Acad.，61 (1985)，252-254.

11. S. Kawashima and A.Matsumura，Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion，Commun. Math. Phys.，101 (1985), 97-127.

10. Y. Shizuta and S. Kawashima，Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation，Hokkaido Math. J.，14 (1985)，249-275.

9. T. Umeda，S. Kawashima and Y. Shizuta，On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics, Japan J. Appl. Math.，1 (1984)，435-457.

8. S. Kawashima, Smooth global solutions for two-dimensional equations of electromagneto-fluid dynamics，Japan J. Appl. Math.，1 (1984)，207-222.

7. S. Kawashima，Global existence and stability of solutions for discrete velocity models of the Boltzmann equation，Recent Topics in Nonlinear PDE (M. Mimura and T. Nishida, eds.), Lecture Notes in Num. Appl. Anal., 6, Kinokuniya, (1983), 59-85.

6. M. Okada and S. Kawashima，On the equations of one-dimensional motion of compressible viscous fluids，J. Math. Kyoto Univ.，23 (1983), 55-71.

5. S. kawashima and M.OKada，Smooth global solutions for the one-dimensional equations in magnetohydrodynamics，Proc. Japan Acad.， 58 (1982)，384-387.

4. S. Kawashima and T. Nishida, Global solutions to the initial value problem for the equations of one-dimensional motion of viscous polytropic gases, J. Math. Kyoto Univ., 21 (1981), 825-837.

3. S. Kawashima, The asymptotic equivalence of the Broadwell Model equation and its Navier-Stokes model equation, Japan. J. Math., 7 (1981), 1-43.

2. S. Kawashima，Global solution of the initial value problem for a discrete velocity model of the Boltzmann equation， Proc. Japan Acad.，57 (1981)，19-24.

1. S. Kawashima，A. Matsumura and T. Nishida，On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation，Commun. Math. Phys.，70 (1979)，97-124.