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Hyperbolic Conservation Laws and L2

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

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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.

Dedicated to Ian H. Sloan on the occasion of his 80th birthday.

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Acknowledgements

In a different context, Feride Tığlay suggested the idea of looking for bounds of the form (17). We are indebted to her and to John Holmes for helpful conversations about this problem.

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Authors and Affiliations

  1. Mathematics Department, The Ohio State University, Columbus, OH, USA

    Barbara Lee Keyfitz

  2. Bank of America, Charlotte, NC, USA

    Hao Ying

Authors
  1. Barbara Lee Keyfitz
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  2. Hao Ying
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Correspondence to Barbara Lee Keyfitz .

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Editors and Affiliations

  1. School of Mathematics and Statistics, University of New South Wales, Sydney, Australia

    Josef Dick

  2. School of Mathematics and Statistics, University of New South Wales, Sydney, Australia

    Frances Y. Kuo

  3. Department of Computer Science, Columbia University, New York, USA

    Henryk Woźniakowski

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Keyfitz, B.L., Ying, H. (2018). Hyperbolic Conservation Laws and L2. In: Dick, J., Kuo, F., Woźniakowski, H. (eds) Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan. Springer, Cham. https://doi.org/10.1007/978-3-319-72456-0_31

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