Abstract
We consider the linearized hydrodynamic system for an ideal contractible fluid and a linearized system of Maxwell equations with nonlinear current J ( ρ , E ) . We suggest conditions on the symbol of the linear system that generalize the properties of symbols of the linearized systems under consideration. Under these conditions, we prove an existence and uniqueness theorem for linear nonstrictly hyperbolic systems. Linearization of nonlinear hyperbolic systems is used to study waves and their stability under the action of high-frequency perturbations of initial data in physical media. The linearization of a nonlinear real firstorder system for some smooth solution yields a real first-order hyperbolic system L of the form
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