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High order regularity for solutions of the inviscid burgers equation

Hyperbolic P.D.E. Theory

Part of the Lecture Notes in Mathematics book series (LNM,volume 1402)

Abstract

We discuss a recent Besov space regularity theory for discontinuous, entropy solutions of quasilinear, scalar hyperbolic conservation laws in one space dimension. This theory is very closely related to rates of approximation in L 1 by moving grid, finite element methods. In addition, we establish the Besov space regularity of solutions of the inviscid Burgers equation; the new aspect of this study is that no assumption is made about the local variation of the initial data.

Keywords

  • Besov Space
  • Algebraic Curf
  • Entropy Solution
  • Piecewise Polynomial
  • Springer Lecture Note

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© 1989 Springer-Verlag

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DeVore, R.A., Lucier, B.J. (1989). High order regularity for solutions of the inviscid burgers equation. In: Carasso, C., Charrier, P., Hanouzet, B., Joly, JL. (eds) Nonlinear Hyperbolic Problems. Lecture Notes in Mathematics, vol 1402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083873

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  • DOI: https://doi.org/10.1007/BFb0083873

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51746-7

  • Online ISBN: 978-3-540-46800-4

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