High order regularity for solutions of the inviscid burgers equation

  • Ronald A. DeVore
  • Bradley J. Lucier
Hyperbolic P.D.E. Theory

DOI: 10.1007/BFb0083873

Part of the Lecture Notes in Mathematics book series (LNM, volume 1402)
Cite this paper as:
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

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 L1 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.

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Ronald A. DeVore
    • 1
  • Bradley J. Lucier
    • 2
  1. 1.Department of MathematicsUniversity of South CarolinaColumbia
  2. 2.Department of MathematicsPurdue UniversityWest Lafayette

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