Validity of Nonlinear Geometric Optics for Entropy Solutions of Multidimensional Scalar Conservation Laws

Authors: Gui-Qiang Chen, Stephane Junca, and Michel Rascle

Title: Validity of Nonlinear Geometric Optics for Entropy Solutions of Multidimensional Scalar Conservation Laws

Abstract
Nonlinear geometric optics with various frequencies for entropy solutions 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 involved, in particular, nonlinear propagations of oscillations with ultrahigh frequencies. The validity of nonlinear geometric optics for entropy solutions of multidimensional scalar conservation laws is justified.

This article has appeared in:
JDE vol. 20, pages (2004)

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Author Address
    Gui-Qiang Chen
    Department of Mathematics
    Northwestern University
    Evanston, IL 60208-2730
    gqchen@math.nwu.edu