Decay of Positive Waves for $n \times n$ Hyperbolic Systems of Balance Laws

TL;DR

This paper establishes decay estimates for entropy solutions of hyperbolic balance law systems, using wave-front tracking and a discrete lattice approach to handle source terms.

Contribution

It introduces Oleb1nik-type decay estimates for $n\times n$ hyperbolic systems with balance laws, employing a novel wave-front tracking method with source terms treated as nonconservative products.

Findings

Proves decay estimates for entropy solutions.

Develops a wave-front tracking procedure for systems with source terms.

Handles source terms as nonconservative products on a lattice.

Abstract

We prove Ole\u \i nik-type decay estimates for entropy solutions of $n\times n$ strictly hyperbolic systems of balance laws built out of a wave-front tracking procedure inside which the source term is treated as a nonconservative product localized on a discrete lattice.