Time Memory Effect in Entropy Decay of Ornstein-Uhlenbeck Operators
Keywords:
Memory kernels, Ornstein-Uhlenbeck operators, entropy estimates, logarithmic Sobolev inequalities.Abstract
We investigate the effect of memory terms on the entropy decay of the solutions to diffusion 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.
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