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Convergence rates to nonlinear diffusion waves for weak entropy solutions to p-system with damping 被引量：8

Convergence rates to nonlinear diffusion waves for weak entropy solutions to p-system with damping
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摘要 This paper studies the asymptotic behavior ofweak entropy solutions to the Cauchy problem of the so-called p-system with damping. The convergence rates to nonlinear diffusion waves for weak entropy solutions are obtained in L∞-norm or L2-norm. These convergence rates are the same to the decay rates of smooth solution obtained by Nishihara. They are proved by using the vanishing viscosity method and the elementary L2-energy method. This paper studies the asymptotic behavior of weak entropy solutions to the Cauchy problem of the so-called p-system with damping. The convergence rates to nonlinear diffusion waves for weak entropy solutions are obtained in L∞norm or L2 -norm. These convergence rates are the same to the decay rates of smooth solution obtained by Nishihara. They are proved by using the vanishing viscosity method and the elementary L2-energy method.
作者 朱长江
机构地区 Laboratory of Nonlinear Analysis
出处 《Science China Mathematics》 SCIE 2003年第4期562-575,共14页 中国科学：数学（英文版）
基金 The research was supported by the Zheng Ge Ru Foundation of CUHK and two grants from the National Natural Science Foundation of China(#10171037) sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars State Education Ministry respectively.
关键词 WEAK entropy solution diffusion wave convergence rate VANISHING VISCOSITY method energy method. weak entropy solution diffusion wave convergence rate vanishing viscosity method energy method
分类号 O175 [理学—基础数学]
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参考文献18

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同被引文献23

  • 1ZHU Changjiang JIANG Mina.L^p-decay rates to nonlinear diffusion waves for p-system with nonlinear damping[J].Science China Mathematics,2006,49(6):721-739. 被引量：11
  • 2ALI G,TORCICOLLO I.Global solutions to a hydrodynamical model for semiconductors in Lagrangian mass coordinates[EB/OL].[2010-01-15].http://www.na.iac.cnr.it/rapprti/2006/RT312-06.pdf,2006.
  • 3YING L A,WANG C H.Global solution of the cauchy problom for a nonhomogeneous quasilinear hyperbolic system[J].Comm Pure Appl Math,1980,33(5):579-597.
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  • 5TETU MAKINO,KIYOSHI,MIZOHATA,SEIJI UKAI.The Global Weak Solutions of the Compressible Euler Equation with Spherical Symnetry[R].日本:数理解析研究所,1992:1-28.
  • 6DENIS SERRE.Systems of Conservation Laws[M].英国:剑桥大学出版社,2000:146-182.
  • 7KENJI NISHIHARA.Boundary Effect on Asymptotic Behavior of Solutions to the p-system with Linear Damping[R].日本:数理解析研究所,1999:78-94.
  • 8KENJI NISHIHARA.Lp-convergence Rate to Nonlinear Diffusion Wavea for p-system with Damping[R].日本:数理解析研究所,1999:95-113.
  • 9JIALE HUA,TDNG YANG.An improved convergence rate of Glimm scheme for general systems of hyperbolic conservation laws[J].Journal of Differential Equations,2006,231(1):92-107.
  • 10LING HSIAO,TAO LUO,TONG YANG.Clobal BV solutions of compressible euler equations with spherical symmetry and damping[J].Journal of Differential Equations,1998,146(1):203-225.

引证文献8

二级引证文献15

Science China Mathematics
2003年 第4期

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