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

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¹,
孔德兴²

1.
华北水利水电学院数学与信息科学系,郑州 450008;2.上海交通大学应用数学系,上海 200030

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
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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

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

LIU Fa-gui¹,
KONG De-xing²

1.
Department of Mathematics and Information Sciences, North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450008, P. R. China;

摘要

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．
- 多孔介质 /
- 可压缩流体力学 /
- 方程组 /
- 经典解 /
- 整体存在性 /
- 破裂
Abstract: By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small' solution.
- porous media /
- compressible adiabatic flow /
- system of equations /
- classical solution /
- global existence /
- blow-up

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参考文献(12)

[1]	LIU Tai-ping. Development of singularities in the nonlinear wave for quasilinear partial differential equations[J].J Differential Equations,1979,33(2):92—111. doi: 10.1016/0022-0396(79)90082-2
[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.
[7]	LIN Long-wei,ZHENG Yong-shu.Existence and nonexistence of global smooth solutions for quasilinear hyperbolic system[J].Chinese Ann Math，Ser B,1988,9(4):372—377.
[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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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

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).

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

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留言板

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

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).

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出版历程

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

计量

出版历程

目录

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).