Applied Mathematics and Mechanics

, Volume 28, Issue 9, pp 1191–1198 | Cite as

Two-dimensional non-selfsimilar initial value problem for adhesion particle dynamics

  • Sun Wen-hua  (孙文华)Email author
  • Sheng Wan-cheng  (盛万成)


A two-dimensional non-selfsimilar initial value problem for adhesion particle dynamics with two pieces of constant states separated by a circular ring is considered. By using the generalized characteristic method and the generalized Rankine-Hugoniot relation, which is a system of ordinary equations, the global solution which includes delta-shock waves and vacuum is constructed.

Key words

Adhesion particle dynamics generalized Rankine-Hugoniot relation entropy condition delta-shock vacuum 

Chinese Library Classification


2000 Mathematics Subject Classification

35L65 76N10 


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  1. [1]
    Weinan E, Rykov Yu G, Sinai Ya G. Generalized variational principles, global weak solutions and behavior with randon initial data for systems of conservation laws arising in adhesion particle dynamics[J]. Comm Phys Math, 1996, 177:349–380.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Shandarin F, Zeldovich Ya B. The large-scale structure of the universe: turbulence, intermittency, structures in a self-gravitation medium[J]. Reviews of Modern Physics, 1989, 61(2):185–220.CrossRefMathSciNetGoogle Scholar
  3. [3]
    Li Y, Cao Y. Second order “large particle” difference method[J]. Science in China, Series A, 1985, 8:1024–1035.MathSciNetGoogle Scholar
  4. [4]
    Sheng W, Zhang T. The Riemann problem for transportation equation in gas dynamics[J]. Mem Amer Math Soc, 1999, 137(654).Google Scholar
  5. [5]
    Li J, Zhang T, Yang S, The two-dimensional Riemann problem in gas dynamics[M]. New York: Longman Scientific and Technical, 1998.Google Scholar
  6. [6]
    Korchinski D J. Solutions of a Riemann problem for a 2 × 2 system of conservation laws possessing classical solutions[D]. Ph D Dissertation, Adelphi University, 1977.Google Scholar
  7. [7]
    Floch P Le. An existence and uniqueness result for two nonstrictly hyperbolic systems[M]. In: “Nonlinear Evolution Equations That Change Type”, IMA Volumes in Mathematics and Its Applications. New York/Berlin: Springer-Verlag, 1990, 27.Google Scholar
  8. [8]
    Tan D, Zhang T, Zheng Y. Delta-shock waves as limits of vanishing viscosity ofr hyperbolic system of conservation laws[J]. J Differential Equations, 1994, 112:1–32.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Yang H, Sun W. The Riemann problem with delta initial data for a class of coupled hyperbolic systems of conservation laws[J]. Nonlinear Analysis 2006, doi:10.1016/ Scholar
  10. [10]
    Lax P D. Hyperbolic systems of conservation laws and the mathematical theory of shock waves[J]. SIAM, Philadelphia, 1973.Google Scholar
  11. [11]
    Yang H. Generalized plane delta-shock waves for n-dimensional zero-pressure gas dynamics[J]. J Math Anal Appl, 2001, 260:18–35.zbMATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    Yang X. Research announcements: un-selfsimilar elementary wave and global solutions of a class of multi-dimensional conservation laws[J]. Advances in Mathematics (China), 2005, 34(3):367–369.MathSciNetGoogle Scholar
  13. [13]
    Yang X, Huang F. Two dimensional Riemann problem of simplified Euler equation[J]. Chinese Science Bulletin, 1998, 43(6):441–444 (in Chinese).zbMATHCrossRefMathSciNetGoogle Scholar
  14. [14]
    Yang X. Mulit-dimensional Riemann problem of scalar conservation laws[J]. Acta Mathematica Scientia, 1999, 19(2):190–200.zbMATHMathSciNetGoogle Scholar
  15. [15]
    Yang X. The singular structure of non-selfsimilar global n dimensional burgers equation[J]. Acta Mathematicae Applicatae Sinica (English Series), 2005, 21(3):505–518.zbMATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    Huang F, Wang Z. Well posedness for pressureless flow[J]. Comm Math Phys, 2001, 222(1):117–146.zbMATHCrossRefMathSciNetGoogle Scholar
  17. [17]
    Li J, Zhang T. Generalized Rankine-Hugoniot relations of delta-shocks in solutions of transportation equations[M]. In: Advances in Nonlinear Partial Differential Equations and Related Area, New Jersey: World Sci Publ, 1998, 219–232.Google Scholar
  18. [18]
    Li J, Li W. Riemann problem for the zero-pressure flow in gas dynamics[J]. Progr Natur Sci (English Ed), 2001, 11(5):331–344.MathSciNetGoogle Scholar

Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Sun Wen-hua  (孙文华)
    • 1
    • 2
    Email author
  • Sheng Wan-cheng  (盛万成)
    • 1
  1. 1.Department of MathematicsShanghai UniversityShanghaiP. R. China
  2. 2.School of Mathematics and Information SciencesShandong University of TechnologyZiboP. R. China

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