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GENERALIZED PLANE WAVE SOLUTION FOR MULTI-DIMENSIONAL SCALAR CONSERVATION LAW
Changbo Yang (P. R. China) and Yuguang Xu (P. R. China)
Received December 16, 2007
References:
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[1] E. Conway and J. Smoller, Global solutions of Cauchy problem for quasi-linear first-order equation in several space variables, Comm. Pure Appl. Math. 19 (1996), 95-105.
[2] J. Guckenheimer, Shocks and rarefactions in two space dimensions, Arch. Rational Mech. Anal. 59 (1975), 281-291.
[3] P. D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, SIAM, Philadelphia, 1973.
[4] W. B. Lindquist, The scalar Riemann problem in two spatial dimensions: piecewise smoothness of solutions and its breakdown, SIAM J. Math. Anal. 17 (1986), 1178-1197.
[5] D. Wagner, Riemann problem in two space dimensions for a single conservation law, SIAM J. Math. Anal. 14 (1983), 534-559.
[6] Xiaozhou Yang, Multi-dimensional Riemann problem of scalar conservation law, Acta Math. Sci. 19(2) (1999), 190-200.
[7] T. Zhang and Y. X. Zheng, Two-dimensional Riemann problem for a single conservation law, Trans. Amer. Math. Soc. 312 (1989), 589-619. |
Keywords and phrases:
generalized plane solution, rarefaction wave, shock, entropy condition. |
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