Singularity Formation for a System of Conservation Laws in Two Space Dimensions

Singularity Formation for a System of Conservation Laws in Two Space Dimensions

We study singularity formation for the 2×2 systemut+(u2)x+(uv)y=0 andvt+(uv)x+(v2)y=0. Our analysis is based on the argument, due to J. Keller and L. Ting (1966,Comm. Pure. Appl. Math.19, 371–420), about the evolution along a characteristic of the compression rate of nearby characteristics. This sys...

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Veröffentlicht in:Journal of mathematical analysis and applications 1996-06, Vol.200 (3), p.538-547
Hauptverfasser: Lopes-Filho, M.C., Nussenzveig Lopes, H.J.
Format: Artikel
Sprache:eng
Schlagworte:
Exact sciences and technology
Mathematical analysis
Mathematics
Partial differential equations
Sciences and techniques of general use
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Zusammenfassung:We study singularity formation for the 2×2 systemut+(u2)x+(uv)y=0 andvt+(uv)x+(v2)y=0. Our analysis is based on the argument, due to J. Keller and L. Ting (1966,Comm. Pure. Appl. Math.19, 371–420), about the evolution along a characteristic of the compression rate of nearby characteristics. This system is one of a class of systems, called partially aligned, which exhibit a degenerate characteristic structure where a pair of directions replaces the usual cone at every point.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.1996.0223