# Reverse norms and L infinity exponential decay for a class of degenerate evolution systems arising in kinetic theory

## TL;DR

This paper investigates the exponential decay to equilibrium in degenerate evolution equations related to kinetic theory, introducing a reverse L infinity norm approach to analyze stability and decay properties.

## Contribution

It develops conditions for constructing a stable manifold using a novel reverse L infinity norm framework for degenerate kinetic evolution equations.

## Key findings

- Established criteria for exponential decay to equilibrium.
- Identified conditions where stable manifold construction succeeds or fails.
- Provided insights into the stability analysis of kinetic models.

## Abstract

We consider the question of exponential decay to equilibrium of solutions of an abstract class of degenerate evolution equations on a Hilbert space modeling the steady Boltzmann and other kinetic equations. Specifically, we provide conditions suitable for construction of a stable manifold in a particular "reverse L infinity norm" and examine when these do and do not hold.