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Article Dans Une Revue Journal of Hyperbolic Differential Equations Année : 2005

High order geometric smoothness for conservation laws.

Résumé

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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Dates et versions

hal-00137883 , version 1 (22-03-2007)

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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, 2005, 2, pp 39-59. ⟨hal-00137883⟩
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