# A "forward-in-time" quadratic potential for systems of conservation laws

## TL;DR

This paper introduces a novel quadratic interaction potential for hyperbolic conservation laws that depends only on current and future solution profiles, aiding in bounding wave speed changes during interactions.

## Contribution

It constructs a forward-in-time quadratic potential that improves analysis of wave interactions in conservation laws, unlike traditional methods dependent on past data.

## Key findings

- Provides a new potential function for wave interaction analysis
- Bounds wave speed changes at each interaction
- Enhances understanding of solution dynamics in conservation laws

## Abstract

A quadratic interaction potential $t \mapsto \Upsilon(t)$ for hyperbolic systems of conservation laws is constructed, whose value $\Upsilon(\bar t)$ at time $\bar t$ depends only on the present and the future profiles of the solution and not on the past ones. Such potential is used to bound the change of the speed of the waves at each interaction.