Remarks on the Cauchy problem for first order hyperbolic systems with constant coefficient principal part

Abstract In this article we shall introduce the results obtained in 16], i.e., we shall give a necessary and sufficient condition that the Cauchy problem for first order hyperbolic systems with constant coefficient principal part is C^∞ well-posed under the maximal rank condition (see the condition (R) below). We shall also give a simple sufficient condition without any assumptions on the rank. Keywords: Hyperbolic system, Cauchy problem, Constant coefficient principal part