# On decay of entropy solutions to multidimensional conservation laws

## TL;DR

This paper proves that entropy solutions to certain multidimensional conservation laws with continuous flux decay over time under a specific nonlinearity condition, advancing understanding of long-term behavior.

## Contribution

It establishes decay results for entropy solutions in multidimensional scalar conservation laws with continuous flux under a genuine nonlinearity assumption.

## Key findings

- Entropy solutions decay over time under the given conditions.
- Decay is proven for laws with merely continuous flux.
- The result applies to a broad class of multidimensional conservation laws.

## Abstract

Under a precise genuine nonlinearity assumption we establish the decay of entropy solutions of a multidimensional scalar conservation law with merely continuous flux.