On decay of entropy solutions to multidimensional conservation laws in the case of perturbed periodic initial data

TL;DR

This paper proves that entropy solutions to certain multidimensional conservation laws decay over time when initial data is a combination of periodic functions and functions vanishing at infinity, under a specific nonlinearity condition.

Contribution

It establishes decay results for entropy solutions with continuous flux and mixed initial data, extending understanding of long-term behavior in multidimensional conservation laws.

Findings

Entropy solutions decay over time under given conditions

Decay holds for initial data combining periodic and vanishing functions

Results depend on a genuine nonlinearity assumption

Abstract

Under a precise genuine nonlinearity assumption we establish the decay of entropy solutions of a multidimensional scalar conservation law with merely continuous flux and with initial data being a sum of periodic function and a function vanishing at infinity (in the sense of measure).