Hyperbolic Systems

In this chapter, we will provide a brief overview of the nature of the differential systems we have presented, focusing on the study of the class of equations known as hyperbolic. This class includes the Euler equations, thermoelasticity equations (when thermal conductivity is negligible), and the system governing heat propagation with the Cattaneo equation. Later, we will introduce the method of characteristics to determine the solution of the wave equation in one spatial dimension and, more generally, for a generic linear homogeneous hyperbolic system. As an example of a nonlinear hyperbolic equation, we will present the Burgers’ equation, showing that regular solutions exist only for a finite time (critical time).