# Long-time behavior of a nonlocal Cahn-Hilliard equation with reaction

## TL;DR

This paper investigates the long-term dynamics of a nonlocal Cahn-Hilliard system with singular potential, demonstrating the existence of global and exponential attractors and convergence to equilibrium states.

## Contribution

It establishes the existence of finite-dimensional global and exponential attractors and proves convergence to equilibrium for specific reaction terms in the nonlocal Cahn-Hilliard model.

## Key findings

- Existence of a global attractor with finite fractal dimension.
- Existence of an exponential attractor.
- Convergence to equilibrium states for certain reaction terms.

## Abstract

In this paper we study the long-time behavior of a nonlocal Cahn-Hilliard system with singular potential, degenerate mobility, and a reaction term. In particular, we prove the existence of a global attractor with finite fractal dimension, the existence of an exponential attractor, and convergence to equilibria for two physically relevant classes of reaction terms.