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Exponential decay of a first order linear Volterra equation

Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy

This contribution is part of the Special Issue: Partial Differential Equations from theory to applications—Dedicated to Alberto Farina, on the occasion of his 50th birthday
Guest Editors: Serena Dipierro; Luca Lombardini
Link: http://www.aimspress.com/newsinfo/1396.html

Special Issues: Partial Differential Equations from theory to applications—Dedicated to Alberto Farina, on the occasion of his 50th birthday

We consider the linear Volterra equation of the first order in time $$\dot u(t)+\int_0^t g(s)A u(t-s) d s=0$$ where $A$ is a positive bounded operator on a Hilbert space $H$. The exponential decay of the related energy is shown to occur, provided that the kernel $g$ is controlled by a negative exponential.
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© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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