THE RIEMANN PROBLEM FOR A TWO-DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS WITH NON-CLASSICAL WEAK SOLUTIONS: SOME ONE-J AND NON-R INITIAL DATA

Abstract

Abstract: The Riemann problem for a two-dimensional 2×2 nonstrictly hyperbolic system of nonlinear conservation laws has been considered for constant initial data having discontinuities on three rays with vertex at the origin. The solutions are constructed for some one-J and non-R initial data. One kind of new discontinuity, which is labelled as the δ-shock wave, appears in some solutions. The δ-shock wave is a discontinuity plane that is the suport of a generalized function.

Key words: Riemann problem, conservation laws, δ-shock wave

Hu Jiaxin. THE RIEMANN PROBLEM FOR A TWO-DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS WITH NON-CLASSICAL WEAK SOLUTIONS: SOME ONE-J AND NON-R INITIAL DATA[J].Acta mathematica scientia,Series B, 1997, 17(4): 361-375.

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THE RIEMANN PROBLEM FOR A TWO-DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS WITH NON-CLASSICAL WEAK SOLUTIONS: SOME ONE-J AND NON-R INITIAL DATA

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