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In this note, we consider the Riemann problem for a two-dimensional nonstrictly hyperbolic system of conservation laws. Without the restriction that each jump of the initial data projects one planar elementary wave, six topologically distinct solutions are constructed by applying the generalized characteristic analysis method, in which the delta shock waves and the vacuum states appear. Moreover we demonstrate that the nature of our solutions is identical with that of solutions to the corresponding one-dimensional Cauchy problem, which provides a verification that our construction produces the correct global solutions.
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참고문헌 (24)
참고문헌 신청
A. Bressan / 2000 / Hyperbolic Systems of Conservation Laws: The One-dimensional Cauchy Problem / Oxford University Press
C. Shen / 2009 / Interactions of delta shock waves for the transport equations with split delta functions / J. Math. Anal. Appl 351 (2) : 747 ~ 755
C. Shen / 2010 / Formation of delta shocks and vacuum states in the vanishing pressure limit of Riemann solutions to the perturbed Aw-Rascle model / J. Differential Equation
C. Shen / 2011 / Global structure of Riemann solutions to a system of two-dimensional hyperbolic conservation laws / Nonlinear Anal 74 (14) : 4754 ~ 4770
D. Tan / 1994 / -dimensional Riemann problem for a hyperbolic system of nonlinear conservation laws, (I): Four-J cases; (II): Initial data consists of some rar- efaction / J
C. Shen / 2009 / Interactions of delta shock waves for the transport equations with split delta functions / J. Math. Anal. Appl 351 (2) : 747 ~ 755
C. Shen / 2010 / Formation of delta shocks and vacuum states in the vanishing pressure limit of Riemann solutions to the perturbed Aw-Rascle model / J. Differential Equation
C. Shen / 2011 / Global structure of Riemann solutions to a system of two-dimensional hyperbolic conservation laws / Nonlinear Anal 74 (14) : 4754 ~ 4770
D. Tan / 1994 / -dimensional Riemann problem for a hyperbolic system of nonlinear conservation laws, (I): Four-J cases; (II): Initial data consists of some rar- efaction / J
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