Two Dimensional Non-Selfsimilar Initial Value Problem for Adhesion Particle Dynamics

SUN Wen-hua; SHENG Wan-cheng

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SUN Wen-hua, SHENG Wan-cheng. Two Dimensional Non-Selfsimilar Initial Value Problem for Adhesion Particle Dynamics[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1063-1070.

Citation:

SUN Wen-hua, SHENG Wan-cheng. Two Dimensional Non-Selfsimilar Initial Value Problem for Adhesion Particle Dynamics[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1063-1070.

Citation:

SUN Wen-hua, SHENG Wan-cheng. Two Dimensional Non-Selfsimilar Initial Value Problem for Adhesion Particle Dynamics[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1063-1070.

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Two Dimensional Non-Selfsimilar Initial Value Problem for Adhesion Particle Dynamics

SUN Wen-hua^1,2,
SHENG Wan-cheng¹

1.
Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;

Received Date: 2006-07-05
Rev Recd Date: 2007-05-18
Publish Date: 2007-09-15

Abstract

Abstract

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

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References(18)

References

[1]	Weinan E,Guo Y Rykov,Sinai Ya G. Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics[J].Comm Phys Math,1996,177:349-380. doi: 10.1007/BF02101897
[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. doi: 10.1103/RevModPhys.61.185
[3]	李荫藩.第二阶“大粒子”差分法[J].中国科学A辑，1985,28(8):729-739.
[4]	Sheng W, Zhang T. The Riemann problem for transportation equation in gas dynamics[J].Mem Amer Math Soc,1999,137(654):1-77.
[5]	Li J,Yang S, Zhang T.The Two-Dimensional Riemann Problem in Gas Dynamics[M].Harlow:Longman Scientific and Technical,1998.
[6]	Korchinski D J.Solutions of a Riemann Problem for a 2× 2 System of Conservation Laws Possessing Classical Solutions[D].New York:Adelphi University Thesis,1977.
[7]	Floch Le P.An existence and uniqueness result for two nonstrictly hyperbolic systems[A].In:“Nonlinear Evolution Equations That Change Type,”IMA Volumes in Mathematics and Its Applications[C].New York/Berlin:Springer-Verlag,1990,27.
[8]	Tan D, Zhang T, Zheng Y. Delta-shock waves as limits of vanishing viscosity for hyperbolic system of conservation laws[J].J Differential Equations,1994,112(1):1-32. doi: 10.1006/jdeq.1994.1093
[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/j.na.2006.09.057.
[10]	Lax P D.Hyperbolic systems of conservation laws and the mathematical theory of shock waves[A].Conf Board Math Sci[C].Philadelphia:SLAM,1973,11.
[11]	Yang H. Generalized plane delta-shock waves for n-dimensional zero-pressure gas dynamics[J].J Math Anal and Appl,2001,260(1):18-35. doi: 10.1006/jmaa.2000.7426
[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.
[13]	杨小舟, 黄飞敏.简化Euler方程的二维Riemann问题[J].科学通报,1998,43(6):441-444.
[14]	Yang X. Mulit-dimensional Riemann problem of scalar conservation laws[J].Acta Mathematica Scientia,1999,19(2):190-200.
[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.
[16]	Huang F,Wang Z.Well posedness for pressureless flow[J].Comm Math Phys,2001,222(1):117-146. doi: 10.1007/s002200100506
[17]	Li J, Zhang T. Generalized Rankine-Hugoniot relations of delta-shocks in solutions of transportation equations[A].Advances in Nonlinear Partial Differential Equations and Related Area[C].Singapore:World Sci Publ,River Edge, NJ, 1998, 219-232.
[18]	Li J, Li W. Riemann problem for the zero-pressure flow in gas dynamics[J].Progr Natur Sci,2001,11(5):331-344.