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Necessary and sufficient conditions for the existence of shock curves of hyperbolic 1‐conservation laws
Author(s) -
Chang P. H.,
van der Vooren A. I.
Publication year - 1981
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670030119
Subject(s) - conservation law , mathematics , shock (circulatory) , singularity , mathematical analysis , shock wave , hyperbolic partial differential equation , section (typography) , law , partial differential equation , mechanics , physics , medicine , political science , advertising , business
We present three conditions for the existence of shock curves of hyperbolic 1‐conservation laws. If at least two of the conditions hold, then shock curves exist uniquely in the classical sense. We present an example (Example 2, Section 4) for which two of the conditions do not hold and a new kind of singularity occurs. In Remark 1 we present two other conditions similar to the above three conditions which also imply the existence of shock curves.