Abstract
This paper is a survey of some recent development on the zero-pressure gas dynamics. We will state the mechanism of delta-shock and its propagation, construct the solutions of one-dimensional and two-dimensional Riemann problems, and then prove the existence of solutions to the general Cauchy problem.
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R. K. Agarwal and D. W. Halt, A modified CUSP scheme in wave/particle split form for unstructured grid Euler flow, Frontiers of Computational Fluid Dynamics, David A. Caughey and Mohamed M. Hafez, (1994), 155–163.
F. Bouchut, On zero pressure gas dynamics, Advances in kinetic theory and computing, Series on Advances in Math. for Appl. Sci., World Scientific, 22 (1994), 171–190.
G. Ben-dor and I. Glass, Domains and boundaries of non-stationary oblique shock wave reflection (1), (2), J. Fluid Mech, 92 (1979), 459–496; 96 (1980), 735–756.
S. Cheng, J. Li and T. Zhang, Explicit construction of measure solutions of the Cauchy problem for transportation equations, Science in China (Series A), 40 (12) (1997), 1287–1299.
S. Cheng, J. Li and T. Zhang, On two-dimensional Riemann problem for zero-pressure gas dynamics, submitted to Comm. Math. Phys., (1997).
S. Cheng, J. Li and T. Zhang, The existence of solutions to two-dimensional Cauchy problem for zero-pressure gas dynamics, preprint, (1998).
Weinan E, Yu. G. Rykov and Ya. G. Sinai, Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics, Comm. Math. Phys., 177 (1996), 349–380.
J. Guckenheimer, Shocks and rarefactions in two space dimensions, Arch. Rational Mech. Anal., 59 (1975), 281–291.
J. Li, Generalized Rankine-Hugoniot conditions of delta-shocks and Cauchy problem for transportation equations, Ph.D dissertation, Inst. Math., Academic Sinica, (1996).
J. Li, On the global measure solutions to the zero-pressure gas dynamics, preprint, (1997).
Y. Li and Y. Cao, Second order “large particle” difference method, Science in China (Series A), 28 (8) (1985), 1024–1035.
J. Li and T. Zhang, Generalize Rankine-Hugoniot relations of delta-shocks in solutions of transportation equations, to appear in Proc. Inter. Conf. PDE, edited by G. Q. Chen, (1997).
B. Perthame, Introduction to the collision models in Boltzmann’s theory, preprint, (1996).
S. F. Shandarin and Ya. B. Zeldovich, The large-scale structure of the universe: turbulence, intermittency, structures in a self-gravitating medium,Rev. Mod. Phys., 61 (1989), 185–220.
W. Sheng and T. Zhang, The Riemann problem for transportation equations,accepted for publication in Memoirs of AMS, (1997).
H. Yang and J. Li, Delta-shocks as the limit of solutions of multidimensional zero-pressure gas dynamics, submitted to Proc. Edinburgh Math. Socie., (1997).
Peng Zhang and Tong Zhang, Generalized characteristic analysis and Guckenheimer structure, preprint, (1997).
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Li, J., Zhang, T. (1999). On the Initial-value Problem for Zero-pressure Gas Dynamics. In: Jeltsch, R., Fey, M. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 130. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8724-3_14
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DOI: https://doi.org/10.1007/978-3-0348-8724-3_14
Publisher Name: Birkhäuser, Basel
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