郭俐辉

• 1:新疆大学数学与系统科学学院

摘要(Abstract)：

构造性的得到了广义Chaplygin气体交通流AW-Rascle(AR)模型Riemann问题的解.它包括三种解:前两种解包含R(疏散波)+J(接触间断)和S(激波)+J(接触间断),最后一种解是包含满足广义Rankine-Hugoniot和熵条件的Delta激波解.

关键词(KeyWords)： AW-Rascle模型;Riemann问题;广义Chaplygin气体;线性退化;Delta激波

Abstract:

Keywords:

基金项目(Foundation): Supported by the Scientific Research Program of the Higher Education Institution of Xinjiang(XJEDU2011S02);; the Ph.D Graduate Start Research Foundation of Xinjiang University Funded Project(No.BS100105 and BS090107);; the National Natural Science Foundation of China(11101348)

作者(Author): 郭俐辉

参考文献(References)：

• [1]Aw A,Rascle M.Resurrection of”second order”models of traffic flow[J].SIAM J Appl Math,2000,60:918-938.
• [2]Daganzo C.Requiem for second order fluid appproximations of traffic flow[J].Transportation Res B,1995,29:277-286.
• [3]Greenberg J M,Klar A,Rascle M.Congestion on multilane highways[J].SIAM J Appl Math,2003,63:818-833.
• [4]Garavello M,Piccoli B.Traffic flow on a road network using the Aw-Rascle model[J].Comm Patial Differential Equations,2006,31:243-275.
• [5]Sun M N.Interactions of elementary waves for the Aw-Rascle model[J].SIAM J Appl Math,2009,69(2):1542-1558.
• [6]Chaplygin S.On gas jets[J].Sci Mem Moscow Univ Math Phys,1904,21:1-121.
• [7]Tsien H S.Two dimensional subsonic flow of compressible fluids[J].J Aeron Sci,1939,6:399-407.
• [8]Karman T.Compressibility effects in aerodynamics[J].J Aeron Sci,1941,8:337-365.
• [9]Bedran M L,Soares V,Arau′jo M E.Temperature evolution of the FRW universe filled with modified Chaplygin gas[J].Phys Lett,2008,659:462-465.
• [10]Wu Y B,Yang W Q,Wang C,Wang L.Modified Chaplygin gas as an interacting holographic dark energy model[J].Sci China Phys Mech Astron,2010,53(4):598-606.
• [11]Brenier Y.Solutions with concentration to the Riemann problem for one-dimensional Chaplygin gas equations[J].J Math Fluid Mech,2005,7:326-331.
• [12]Guo L H,Sheng W C,Zhang T.The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system[J].Communications on Pure and Applied Analysis,2010,9:431-458.
• [13]Chang T,Hsiao L.The Riemann problem an Interaction of Waves in Gas Dynamics[M].England:Longman Scientific and Technical,1989.
• [14]Chen G Q,Li Y C.Stability of Riemann solutions with large oscillation for the relativistic Euler equations[J].J Differential Equations,2004,202:332-353.
• [15]Courant R,Friedrichs K O.Supersonic Flow and Shock Waves[M].New York:Wiley,1948.
• [16]Lax P D.Hyperbolic system of conservation laws II[J].Comm Pure Appl Math,1957,10:537-566.
• [17]Li J Q,Zhang T,Yang S L.The two-dimensional Riemann problem in gas dynamics[M].England:Longman Scientific and Technical,1998.
• [18]Serre D.Multidimensional shock interaction for a Chaplygin gas[J].Arch Rational Mech Anal,2009,191:539-577.
• [19]Setare M R.Holographic Chaplygin gas model[J].Phys Lett B,2007,648:329-332.
• [20]Cheng H,Yang H.Riemann problem for the relativistic Chaplygin Euler equations[J].J Math Anal Appl,2011,381:17-26.
• [21]Sheng W C,Zhang T.The Riemann Problem for the Transportation Equations in Gas Dynamics[J].Mem Amer Math Soc,1999,137:654.