Decoupling and definition of the dependency domain of a hyperbolic linear conservation system

Abstract

The equations that govern the behavior of some of the equations of Physics-Mathematics, such as elastic, acoustic and electromagnetic waves, can be reduced to systems of first order PDE's, which result from operating on a second order hyperbolic PDE. In order to solve numerically this type of equations, they can be taken to this type of linear systems of PDE's. Our objective in this article is to present a technique for the transformation of the hyperbolic second order PDE to a linear system of first order PDE's, for the case of any wave equation, as well as the decoupling of such system to reduce them to independent first order PDE's and thus define the domain of dependence of the system, in order to determine the geometric place where it will allow to establish the existence and uniqueness of solution of the initial value problem or Cauchy, associated to the system.