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．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.
-
Key words:
- porous media /
- compressible adiabatic flow /
- system of equations /
- classical solution /
- global existence /
- blow-up
-
[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. -
点击查看大图
计量
- 文章访问数: 2877
- HTML全文浏览量: 136
- PDF下载量: 844
- 被引次数: 0
下载:
