No Access
APPROXIMATING INFINITE DELAY WITH FINITE DELAY
https://doi.org/10.1142/S0219199712500125Cited by:2 (Source: Crossref)
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.
AMSC: 35B40, 45K05, 45M05
