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

Acta mathematica scientia,Series B ›› 1997, Vol. 17 ›› Issue (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

Hu Jiaxin

Young Scientists Laboratory of Mathematical Physics, Wuhan Institute of Physics and Mathematics, Academia Sinica, Wuhan 450071, China

Received:1995-02-17 Revised:1996-04-23 Online:1997-12-25 Published:1997-12-25
Supported by:
Supported by NSFC(Youth).

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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