Published 2006 | Version v1
Journal article Metadata-only

Validity of nonlinear geometric optics for entropy solutions of multidimensional scalar conservation laws

Chen, Gui-Qiang
Junca, Stéphane
Rascle, Michel
Others:
Northwestern University [Evanston]
Laboratoire Jean Alexandre Dieudonné (JAD) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)

Description

Nonlinear geometric optics with various frequencies for entropy solutions only in $L^∞$ of multidimensional scalar conservation laws is analyzed. A new approach to validate nonlinear geometric optics is developed via entropy dissipation through scaling, compactness, homogenization, and $L^1$-stability. New multidimensional features are recognized, especially including nonlinear propagations of oscillations with high frequencies. The validity of nonlinear geometric optics for entropy solutions in $L^∞$ of multidimensional scalar conservation laws is justified.

Abstract

International audience

Additional details

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Created:
February 28, 2023
Modified:
November 30, 2023