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.
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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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