Chapter 6 Nonlocal Initial and Boundary Value Problems: A Survey

Abstract

This chapter presents a survey on nonlocal initial and boundary value problems. The evolution of a physical system in time is described by an initial value problem, that is, a differential equation (ordinary or partial) and an initial condition. In many cases, it is better to have more initial information. The local condition is then replaced by a nonlocal condition that gives better effect than the local initial condition because the measurement given by a nonlocal condition is usually more precise than the only one measurement given by a local condition. The study of initial value problems with nonlocal conditions is of significance because they have applications in the problems of physics and other areas of applied mathematics. Conditions of this type can be applied in the theory of elasticity with better effect than the initial or Darboux conditions.