ABSTRACT
Physical situations described by quantities that vary continuously with respect to their position in space and possibly with time can usually be described in terms of systems of partial differential equations (PDE). These are equations that relate the quantities involved to some of their derivatives with respect to space variables and time. The order of a PDE or system is the order of the highest derivative that occurs in the PDE or system. In the study of PDEs, general solutions are hardly ever known, so instead it is necessary to seek the solution of a PDE in the context of a specific application. When doing this, certain auxiliary conditions must be specified that serve to identify the precise nature of the problem. Any second-order PDE can always be written as a first-order system by introducing its first-order partial derivatives as new dependent variables.
