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多孔介质中可压缩流体力学方程组经典解的整体存在性与破裂现象

刘法贵 孔德兴

刘法贵, 孔德兴. 多孔介质中可压缩流体力学方程组经典解的整体存在性与破裂现象[J]. 应用数学和力学, 2004, 25(6): 643-652.
引用本文: 刘法贵, 孔德兴. 多孔介质中可压缩流体力学方程组经典解的整体存在性与破裂现象[J]. 应用数学和力学, 2004, 25(6): 643-652.
LIU Fa-gui, KONG De-xing. Global Existence and Blow-up Phenomena of Classical Solutions for the System of Compressible Adiabatic Flow Through Porous Media[J]. Applied Mathematics and Mechanics, 2004, 25(6): 643-652.
Citation: LIU Fa-gui, KONG De-xing. Global Existence and Blow-up Phenomena of Classical Solutions for the System of Compressible Adiabatic Flow Through Porous Media[J]. Applied Mathematics and Mechanics, 2004, 25(6): 643-652.

多孔介质中可压缩流体力学方程组经典解的整体存在性与破裂现象

基金项目: 国家自然科学基金资助项目(10001024);国家基础研究资助课题(G2000077306)
详细信息
    作者简介:

    刘法贵(1965- ),男,河南内乡人,教授,博士(联系人.Tel:+86371-5727655-3399;Fax:+86-371-5790220;E-mail:liufagui@ncwu.edu.cn).

  • 中图分类号: O175.27

Global Existence and Blow-up Phenomena of Classical Solutions for the System of Compressible Adiabatic Flow Through Porous Media

  • 摘要: 利用拟线性双曲型方程组极值原理,改进了HSIAO Ling和D.Serre得到的关于多孔介质中可压缩流体力学方程组解的存在性结果,给出了其Cauchy问题的一个关于经典解整体存在和破裂的完整结果.这些结果说明强耗散有助于“小”解的光滑性.
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    [2] ZHAO Yan-chun. Global smooth solutions for one dimensional gas dynamics systems[R]. IMA Preprint #545,University of Minnesuta,1989.
    [3] KONG De-xing.Cauchy Problem for Quasilinear Hyperbolic Systems[M].MSJ Memoirs No 6.Tokyo:the Mathematical Society of Japan,2000.
    [4] KONG De-xing.Life-span of the classical solutions of nonlinear hyperbolic systems[J].J Partial Differential Equations,1996,11(2):221—240.
    [5] Nishida T.Nonlinear Hyperbolic Equations and Related Topics in Fluid Dynamics[M].Paris-Sud:Publications Mathématiqées D'osay 78-02,1978.
    [6] Slemrod M. Instability of steady shearing flows in a nonlinear viscolastic fluid[J].Arch Rational Mech Anal,1978,68(3):211—225.
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    [8] 王剑华,李才中.具耗散拟线性双曲型方程组整体光滑可解性与奇性形成[J].数学年刊,A辑,1988,9(5):509—523.
    [9] HSIAO Ling,Serre D.Global existence of solutions for the systems of compressible adiabatic flow through porous media[J].SIAM J Math Anal,1996,27(1):70—77. doi: 10.1137/S0036141094267078
    [10] 郑永树.具耗散一维气体动力学方程组整体光滑解[J].数学年刊,A辑,1996,17(2):155—162.
    [11] KONG De-xing. Maximum principles for quasilinear hyperbolic systems and its applications[J].Nonlinear Analysis: Theory, Methods and Applications,1998,32(9):871—880. doi: 10.1016/S0362-546X(97)00534-8
    [12] LI Ta-tsien,YU Wen-ci.Boundary Value Problems for Quasilinear Hyperbolic Systems[M].Mathematics Series V,Duke University Press,1985.
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  • 被引次数: 0
出版历程
  • 收稿日期:  2001-11-27
  • 修回日期:  2003-12-08
  • 刊出日期:  2004-06-15

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