Compactness and Asymptotic Behavior of Entropy Solutions without Locally Bounded Variation for Hyperbolic Conservation Laws

Authors: Gui-Qiang Chen

Title: Compactness and Asymptotic Behavior of Entropy Solutions without Locally Bounded Variation for Hyperbolic Conservation Laws

Abstract
We discuss some recent developments and ideas in studying the compactness and asymptotic behavior of entropy solutions without locally bounded variation for nonlinear hyperbolic systems of conservation laws. Several classes of nonlinear hyperbolic systems with resonant or linear degeneracy are analyzed. The relation of the asymptotic problems to other topics such as scale-invariance, compactness of solutions, and singular limits is described.

This article has appeared in:
Hyperbolic Problems: Theory, Numerics, Applications (Volume 1), International Series of Numerical Mathematics 129, 139-148, Birkhauser Verlag: Basel, (eds.) Michael Fey and Rolf Jeltsch, 1999

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