Minimax Theory and its Applications 06 (2021), No. 2, 173--190
Copyright Heldermann Verlag 2021
Time Memory Effect in Entropy Decay of Ornstein-Uhlenbeck Operators
Antonio Agresti
Dept. of Mathematics Guido Castelnuovo, Sapienza University of Rome, 00185 Roma, Italy
agresti@mat.uniroma1.it
Paola Loreti
SBAI Department, Sapienza University of Rome, 00161 Roma, Italy
paola.loreti@sbai.uniroma1.it
Daniela Sforza
SBAI Department, Sapienza University of Rome, 00161 Roma, Italy
daniela.sforza@sbai.uniroma1.it
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.
Keywords: Memory kernels, Ornstein-Uhlenbeck operators, entropy estimates, logarithmic Sobolev inequalities.
MSC: 45K05, 47G20, 54C70.
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