Departamento de Matemáticas
Puras y Aplicadas, Universdad Simón Bolívar, Caracas 1080-A, Venezuela
Copyright © 2010 Raúl Manzanilla et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A semigroup theory for a differential equation with delayed and advanced arguments is developed, with a detailed description of the infinitesimal generator. This in turn allows to study the exact controllability of the equation, by rewriting it as a classical Cauchy problem.