Global Existence for Nonlinear Hyperbolic Systems of Kirchhoff Type

In this paper we prove the global solvability of the Cauchy problem, with small and suitably smooth initial data, for nonlinear hyperbolic systems with integro- differential coefficients of Kirchhoff type. This extends to a wide class of nonlinear hyperbolic equations some results in [4, 5, 7] and [10]. Our method is similar to the technique employed by Greenberg & Hu in [10] in the case of the classical Kirchhoff equation.