Asymptotic stability of Riemann waves for conservation laws

Abstract.

We are concerned with the asymptotic behavior of entropy solutions of conservation laws. A new notion about the asymptotic stability of Riemann solutions is introduced, and corresponding analytical frameworks are developed. The correlation between the asymptotic problem and many important topics in conservation laws and nonlinear analysis is recognized and analyzed, such as zero dissipation limits, uniqueness of entropy solutions, entropy analysis, and divergence-measure fields in $L^\infty$. Then this theory is applied to understanding the asymptotic behavior of entropy solutions for many important systems of conservation laws.