## 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