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Hyperbolic Conservation Laws and L2

In: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan

Author

Listed:
  • Barbara Lee Keyfitz

    (The Ohio State University, Mathematics Department)

  • Hao Ying

    (Bank of America)

Abstract

Taking as background the fact that conservation laws in a single space variable are well-posed in the space of functions of bounded variation, while multidimensional systems enjoy short-time well-posedness in Sobolev spaces H s, we attempt to resolve the discrepancies between these two theories by exploring what can be said about stability of one-dimensional systems in L 2. We summarize some positive results for special cases, and also show by a conterexample that there is no straightforward way to resolve the difficulty.

Suggested Citation

  • Barbara Lee Keyfitz & Hao Ying, 2018. "Hyperbolic Conservation Laws and L2," Springer Books, in: Josef Dick & Frances Y. Kuo & Henryk Woźniakowski (ed.), Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, pages 703-720, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-72456-0_31
    DOI: 10.1007/978-3-319-72456-0_31
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