A max-plus fundamental solution semigroup for a class of lossless wave equations

Abstract

A new max-plus fundamental solution semigroup is presented for a class of lossless wave equations. This new semigroup is developed by employing the action principle to encapsulate the propagation of all possible solutions of a given wave equation in the evolution of the value function of an associated optimal control problem. The max-plus fundamental solution semigroup for this optimal control problem is then constructed via dynamic programming, and used to formulate the fundamental solution semigroup for the original wave equation. An application of this semigroup to solving twopoint boundary value problems is discussed via an example.