High order geometric smoothness for conservation laws.

Abstract : The smoothness of the solutions of 1D scalar conservation laws is investigated and it is shown that if the initial value has smoothness of order α in Lq with α > 1 and q = 1/α, this smoothness is preserved at any time t > 0 for the graph of the solution viewed as a function in a suitably rotated coordinate system. The precise notion of smoothness is expressed in terms of a scale of Besov spaces which also characterizes the functions that are approximated at rate N-α in the uniform norm by piecewise polynomials on N adaptive intervals. An important implication of this result is that a properly designed adaptive strategy should approximate the solution at the same rate N-α in the Hausdorff distance between the graphs.
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https://hal.archives-ouvertes.fr/hal-00137883
Contributor : Martin Campos Pinto <>
Submitted on : Thursday, March 22, 2007 - 1:59:08 PM
Last modification on : Wednesday, May 15, 2019 - 3:43:53 AM

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  • HAL Id : hal-00137883, version 1

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Martin Campos Pinto, Albert Cohen, Pencho Petrushev. High order geometric smoothness for conservation laws.. Journal of Hyperbolic Differential Equations, World Scientific Publishing, 2005, 2, pp 39-59. ⟨hal-00137883⟩

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