Classical solutions of hyperbolic functional differential systems

The paper deals with a generalized Cauchy problem for quasi-linear hyperbolic functional differential systems. The unknown function is the functional variable in the system of equations and the partial derivatives appear in the classical sense. A theorem on the local existence of a solution is proved. The initial problem is transformed into a system of functional integral equations for an unknown function and for their partial derivatives with respect to spatial variables. A method of bicharacteristics and integral inequalites are applied.