Asymptotic stability of shock waves and rarefaction waves under periodic perturbations for 1-D convex scalar conservation laws

TL;DR

This paper investigates the long-term stability and decay behavior of shock and rarefaction waves in one-dimensional convex scalar conservation laws when subjected to periodic disturbances.

Contribution

It establishes the asymptotic stability and decay rates of these waves under periodic perturbations, advancing understanding of wave behavior in nonlinear PDEs.

Findings

Shock and rarefaction waves are asymptotically stable under periodic perturbations.

Decay rates of waves are quantitatively characterized.

Results apply to large-time behavior analysis of scalar conservation laws.

Abstract

In this paper we study large time behaviors toward shock waves and rarefaction waves under periodic perturbations for 1-D convex scalar conservation laws. The asymptotic stabilities and decay rates of shock waves and rarefaction waves under periodic perturbations are proved.