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Hyperbolic Conservation Laws and L2

  • Barbara Lee Keyfitz
  • Hao Ying
Chapter

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 Hs, we attempt to resolve the discrepancies between these two theories by exploring what can be said about stability of one-dimensional systems in L2. We summarize some positive results for special cases, and also show by a conterexample that there is no straightforward way to resolve the difficulty.

Notes

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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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematics DepartmentThe Ohio State UniversityColumbusUSA
  2. 2.Bank of AmericaCharlotteUSA

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