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L1 and L8 intermediate asymptotics for scalar conservation laws

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Date
2005
Dewey
Analyse
Sujet
scalar conservation laws; asymptotics; entropy; shocks; weighted L1 norm; self-similar solutions; N-waves; time-dependent rescaling; Rankine-Hugoniot condition; uniform convergence; graph convergence
Journal issue
Asymptotic Analysis
Volume
41
Number
3-4
Publication date
2005
Article pages
189-213
Publisher
IOS Press
URI
https://basepub.dauphine.fr/handle/123456789/6182
Collections
  • CEREMADE : Publications
Metadata
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Author
Dolbeault, Jean
Escobedo, Miguel
Type
Article accepté pour publication ou publié
Abstract (EN)
In this paper, using entropy techniques, we study the rate of convergence of nonnegative solutions of a simple scalar conservation law to their asymptotic states in a weighted L1 norm. After an appropriate rescaling and for a well chosen weight, we obtain an exponential rate of convergence. Written in the original coordinates, this provides intermediate asymptotics estimates in L1, with an algebraic rate. We also prove a uniform convergence result on the support of the solutions, provided the initial data is compactly supported and has an appropriate behaviour on a neighborhood of the lower end of its support.

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