ABSTRACT

This chapter introduces general framework for systems of first-order, quasilinear partial differential equations for the description of physical systems. It analyses the structure of the partial differential equation describing a single physical system. The physical fields become cross-sections of an appropriate fibre bundle, and it is on these cross-sections that the differential equations are written. The chapter describes various structural features of the system of partial differential equations. A key feature of the partial differential equations of physics is their initial-value formulation, that is, their formulation in terms of initial data and ‘time’-evolution. It turns out that this formulation can be carried out in a rather general setting. The most direct way to prove local uniqueness of solutions of a partial differential equation is to show that it admits a hyperbolization.