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L1 and L8 intermediate asymptotics for scalar conservation laws

Dolbeault, Jean; Escobedo, Miguel (2005), L1 and L8 intermediate asymptotics for scalar conservation laws, Asymptotic Analysis, 41, 3-4, p. 189-213

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Type
Article accepté pour publication ou publié
Date
2005
Journal name
Asymptotic Analysis
Volume
41
Number
3-4
Publisher
IOS Press
Pages
189-213
Metadata
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Author(s)
Dolbeault, Jean cc
Escobedo, Miguel
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.
Subjects / Keywords
scalar conservation laws; asymptotics; entropy; shocks; weighted L1 norm; self-similar solutions; N-waves; time-dependent rescaling; Rankine-Hugoniot condition; uniform convergence; graph convergence