Asymptotic behavior of global entropy solutions for nonstrictly hyperbolic systems with linear damping

TL;DR

This paper studies the long-term behavior of entropy solutions to a symmetric hyperbolic system with linear damping, showing they decay to zero in Lp norm as time approaches infinity.

Contribution

It provides a rigorous analysis of the asymptotic decay of solutions for a specific hyperbolic system with damping, extending understanding of their long-term dynamics.

Findings

Entropy solutions tend to zero in Lp norm as t approaches infinity

The decay rate of solutions is established for the symmetric Keyftiz-Kranzer system

The paper confirms the stability of solutions under linear damping

Abstract

In this paper we investigate the large time behavior of the global weak entropy solutions to the symmetric Keyftiz-Kranzer system with linear damping. It is proved that as t tends to infinite the entropy solutions tend to zero in the L p norm