Time memory effect in entropy decay of Ornstein-Uhlenbeck operators

TL;DR

This paper studies how memory effects influence the rate of entropy decay in solutions to equations with Ornstein-Uhlenbeck operators, including various types of memory kernels, and provides sharp decay rates supported by examples and simulations.

Contribution

It introduces a comprehensive analysis of entropy decay under different memory kernels, including Caputo-Fabrizio and stretched exponential functions, with sharp decay rate results.

Findings

Established sharp entropy decay rates for equations with memory effects.

Included numerical simulations validating theoretical results.

Extended analysis to a broad class of memory kernels.

Abstract

We investigate the effect of memory terms on the entropy decay of the solutions to equations with Ornstein-Uhlenbeck operators. Our assumptions on the memory kernels include Caputo-Fabrizio operators and, more generally, the stretched exponential functions. We establish a sharp rate decay for the entropy. Examples and numerical simulations are also given to illustrate the results.