Equations with infinite delay commonly face the philosophical objection of being "unphysical", since a memory of infinite duration conflicts with reality. Indeed, besides common sense, experimental observations on concrete physical models tell that effects from the far past cannot possibly influence the current dynamics of a given system. On the other hand, infinite delay arises quite naturally in the mathematical description of several relevant phenomena. In this note, we propose a possible conceptual solution, showing that infinite delay can be recovered as a limiting case of finite delay on a large time-scale, along with a quantitative control of the discrepancy.

Approximating infinite delay with finite delay

CONTI, MONICA;MARCHINI, ELSA MARIA;PATA, VITTORINO
2012-01-01

Abstract

Equations with infinite delay commonly face the philosophical objection of being "unphysical", since a memory of infinite duration conflicts with reality. Indeed, besides common sense, experimental observations on concrete physical models tell that effects from the far past cannot possibly influence the current dynamics of a given system. On the other hand, infinite delay arises quite naturally in the mathematical description of several relevant phenomena. In this note, we propose a possible conceptual solution, showing that infinite delay can be recovered as a limiting case of finite delay on a large time-scale, along with a quantitative control of the discrepancy.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/639314
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