A New Approach to Equations with Memory |
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| Authors: | Mauro Fabrizio Claudio Giorgi Vittorino Pata |
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| Affiliation: | (1) Dipartimento di Ingegneria, Università degli Studi di Ferrara, 44100 Ferrara, Italy; e-mail;(2) School of Mathematics, Statistics and Computer Science, Dublin Institute of Technology, Dublin, Ireland; e-mail: jmgolden@maths1.kst.dit.ie |
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| Abstract: | We discuss a novel approach to the mathematical analysis of equations with memory, based on a new notion of state. This is the initial configuration of the system at time t = 0 which can be unambiguously determined by the knowledge of the dynamics for positive times. As a model, for a nonincreasing convex function ${G : mathbb{R}^+ to mathbb{R}^+}We discuss a novel approach to the mathematical analysis of equations with memory, based on a new notion of state. This is the initial configuration of the system at time t = 0 which can be unambiguously determined by the knowledge of the dynamics for positive times. As a model, for a nonincreasing convex function G : mathbbR+ ? mathbbR+{G : mathbb{R}^+ to mathbb{R}^+} such that | $G(0) = lim_{sto 0}G(s) > lim_{stoinfty}G(s) >0 $G(0) = lim_{sto 0}G(s) > lim_{stoinfty}G(s) >0 |
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