A fundamental solution for an infinite dimensional two-point boundary value problem via the principle of stationary action

A new approach for solving two-point boundary value problems for conservative infinite dimensional systems is investigated. This new approach seeks to exploit the principle of stationary action in reformulating and solving such problems in the framework of optimal control. A specific and highly simplified problem involving a one dimensional wave equation is considered. The construction of a solution to an attendant optimal control problem is identified as crucial in applying this new approach.