緩和的双曲型保存則系の数学解析
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| Published in | 数学 Vol. 61; no. 3; pp. 248 - 269 |
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| Main Author | |
| Format | Journal Article |
| Language | Japanese |
| Published |
一般社団法人 日本数学会
2009
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| Subjects | |
| Online Access | Get full text |
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| Author | 川島, 秀一 |
|---|---|
| Author_xml | – sequence: 1 fullname: 川島, 秀一 organization: 九州大学大学院数理学研究院 |
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| Copyright | 2009 一般社団法人 日本数学会 |
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| References | [38] S. Ukai, Les solutions globales de l'équation de Boltzmann dans l'espace tout entier et dans le demi-espace, C. R. Acad. Sci. Paris Sér. A-B, 282A (1976), 317–320. [32] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa (3), 13 (1959), 115–162. [33] T. Nishida and K. Imai, Global solutions to the initial value problem for the nonlinear Boltzmann equation, Publ. Res. Inst. Math. Sci., 12 (1976), 229–239. [31] A. Matsumura and T. Nishida, The initial value problem for the equations of motion of compressible viscous and heat-conductive fluids, Proc. Japan Acad. Ser. A Math. Sci., 55 (1979), 337–342. [12] K. Ide and S. Kawashima, Decay property of regularity-loss type and nonlinear effects for dissipative Timoshenko system, Math. Models Methods Appl. Sci., 18 (2008), 1001–1025. [40] W.-A. Yong, Entropy and global existence for hyperbolic balance laws, Arch. Ration. Mech. Anal., 172 (2004), 247–266. [28] A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Appl. Math. Sci., 53, Springer, New York, 1984. [5] K. O. Friedrichs, Symmetric hyperbolic linear differential equations, Comm. Pure Appl. Math., 7 (1954), 345–392. [27] P. D. Lax, Shock waves and entropy, In: Contributions to nonlinear functional analysis, Proceedings of the Symposium held at the Mathematics Research Center, Univ. of Wisconsin, Madison, 1971, (Ed. E. H. Zarantonello), Mathematics Research Center, Publ., no. 27, Academic Press, New York, 1971, pp. 603–634. [34] R. Racke, Lecture on nonlinear evolution equations —— Initial value problems, Braunschweig, Wiesbaden, Vieweg, 1992. [19] S. Kawashima, Large-time behavior of solutions of the discrete Boltzmann equation, Comm. Math. Phys., 109 (1987), 563–589. [26] P. D. Lax, Hyperbolic systems of conservation laws, II, Comm. Pure Appl. Math., 10 (1957), 537–566. [37] S. Ukai, On the existence of global solutions of mixed problem for non-linear Boltzmann equation, Proc. Japan Acad., 50 (1974), 179–184. [6] K. O. Friedrichs and P. D. Lax, Systems of conservation equations with a convex extension, Proc. Nat. Acad. Sci. U. S. A., 68 (1971), 1686–1688. [20] S. Kawashima, The Boltzmann equation and thirteen moments, Japan. J. Appl. Math., 7 (1990), 301–320. [11] K. Ide, K. Haramoto and S. Kawashima, Decay property of regularity-loss type for dissipative Timoshenko system, Math. Models Methods Appl. Sci., 18 (2008), 647–667. [14] T. Kato, Quasi-linear equations of evolution, with applications to partial differential eqations, Spectral Theory and Differential Equations, (ed. W. N. Everitt), Lecture Notes in Math., Springer, 448 (1975), 25–70. [21] S. Kawashima, A. Matsumura and T. Nishida, On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier–Stokes equation, Comm. Math. Phys., 70 (1979), 97–124. [36] 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. [22] S. Kawashima and Y. Shizuta, On the normal form of the symmetric hyperbolic-parabolic systems associated with the conservation laws, Tôhoku Math. J. (2), 40 (1988), 449–464. [8] S. K. Godunov, An interesting class of quasi-linear systems, Dokl. Acad. Nauk SSSR, 139 (1961), 521–523. [39] 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. [16] S. Kawashima, Global existence and stability of solutions for discrete velocity models of the Boltzmann equation, In: Recent topics in nonlinear PDE, Proceedings of the Meeting on nonlinear partial differential equations held at Hiroshima Univ., Hiroshima, 1983, (Eds. M. Mimura and T. Nishida), Lecture Notes in Numerical and Applied Analysis, 6, Kinokuniya Company Ltd., Tokyo, 1984, 59–85. [10] T. Hosono and S. Kawashima, Decay property of regularity-loss type and application to some nonlinear hyperbolic-elliptic system, Math. Models Methods Appl. Sci., 16 (2006), 1839–1859. [17] S. Kawashima, Systems of a hyperbolic-parabolic composite type, with applications to the equations of magnetohydrodynamics, Doctoral Thesis, Kyoto Univ., 1984. [2] S. Chapman and T. G. Cowling, The mathematical theory of non-uniform gases, 3rd ed., London, Cambridge Univ. Press, 1970. [15] T. Kato, Perturbation theory for linear operators, 2nd ed., Springer, Berlin-New York, 1976. [29] A. Matsumura, An energy method for the equations of motion of compressible viscous and heat-conductive fluids, MRC Technical Summary Report, Univ. of Wisconsin-Madison, 2194 (1981), 1–16. [25] S. Kawashima and W.-A. Yong, Decay estimates for hyperbolic balance laws, to appear in Z. Anal. Awend (J. Anal. Appl.). [35] J. E. M. Rivera and R. Racke, Global stability for damped Timoshenko systems, Discrete Contin. Dyn. Syst., 9 (2003), 1625–1639. [18] S. Kawashima, Large-time behaviour of solutions to hyperbolic-parabolic systems of conservation laws and applications, Proc. Roy. Soc. Edinburgh Sect. A, 106 (1987), 169–194. [3] G. Q. Chen, C. D. Levermore and T.-P. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math., 47 (1994), 787–830. [9] B. Hanouzet and R. Natalini, Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy, Arch. Ration. Mech. Anal., 169 (2003), 89–117. [7] R. Gatignol, Théorie cinétique des gaz à répartition discrète de vitesse, Lecture Notes in Physics, 36, Springer, 1975. [1] S. Bianchini, B. Hanouzet and R. Natalini, Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy, Comm. Pure Appl. Math., 60 (2007), 1559–1622. [30] A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ., 20 (1980), 67–104. [24] S. Kawashima and W.-A. Yong, Dissipative structure and entropy for hyperbolic systems of balance laws, Arch. Ration. Mech. Anal., 174 (2004), 345–364. [23] S. Kawashima and Y. Shizuta, The Navier–Stokes equation in the discrete kinetic theory, J. Méc. théor. appl., 7 (1988), 597–621. [4] C. M. Dafermos, Hyperbolic conservation laws in continuum physics, 2nd ed., Springer, Berlin, 2005. [13] T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Rational Mech. Anal., 58 (1975), 181–205. |
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| SubjectTerms | エネルギー評価 エントロピー 双曲型保存則系 安定性 流体力学的近似 消散構造 減衰評価 |
| Title | 緩和的双曲型保存則系の数学解析 |
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