On real hyperbolic systems with characteristics of variable multiplicity

Real hyperbolic systems, with characteristics of variable multiplicity, whose principal symbols have Jordan blocks, are discussed. An existence and uniqueness theorem is presented for linear hyperbolic system. Linearization of nonlinear hyperbolic systems was taken into account for the study of waves. The stability of waves, under the action of high-frequency perturbations of initial data in physical media is observed. The linearization of a nonlinear real first-order system for some smooth solution yields a real first-order hyperbolic system. Such systems admit no estimates with nondegenerate matrices and the solution to the Cauchy problem for system with rapidly oscillating initial data.