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A Stochastic Galerkin Method for the Fokker–Planck–Landau Equation with Random Uncertainties Read chapter Read first chapter

2018 | OriginalPaper | Chapter

On the Longtime Behavior of Almost Periodic Entropy Solutions to Scalar Conservation Laws

Author : Evgeny Yu. Panov

Published in: Theory, Numerics and Applications of Hyperbolic Problems II

Publisher: Springer International Publishing

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Abstract

We found the precise condition for the decay as \(t\rightarrow \infty \) of Besicovitch almost periodic entropy solutions of multidimensional scalar conservation laws. Moreover, in the case of one space variable we establish asymptotic convergence of the entropy solution to a traveling wave (in the Besicovitch norm). Besides, the flux function turns out to be affine on the minimal segment containing the essential range of the limit profile while the speed of the traveling wave coincides with the slope of the flux function on this segment.

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previous chapter On a Relation Between Shock Profiles and Stabilization Mechanisms in a Radiating Gas Model
next chapter Structure Preserving Schemes for Mean-Field Equations of Collective Behavior
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Metadata
Title
On the Longtime Behavior of Almost Periodic Entropy Solutions to Scalar Conservation Laws
Author
Evgeny Yu. Panov
Copyright Year
2018
Book
Theory, Numerics and Applications of Hyperbolic Problems II

Print ISBN: 978-3-319-91547-0

Electronic ISBN: 978-3-319-91548-7

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-91548-7_30

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