Linear Hyperbolic Systems

This chapter is devoted to aspects of linear hyperbolic systems. We have in mind mainly two classes of systems, symmetric hyperbolic and strictly hyperbolic ones. First we discuss these classes of systems with constant coefficients. Fourier analysis coupled with function-theoretical methods imply well-posedness results for different classes of solutions. Then, we treat such systems with variable coefficients. On the one hand we apply the method of characteristics introduced in Chap. 6 to derive a local existence result in time and space variables. On the other hand we discuss the issue of energy estimates and well-posedness for both cases of symmetric hyperbolic and strictly hyperbolic systems.