only on the values of and in the intervals and , respectively, while if , the function has the form

The method has been extended to a fairly wide class of hyperbolic systems of orders one and two--in particular, to systems of the form where and are quadratic symmetric matrices of order , while and are vectors with components.

Darboux-Picard problem

A direct generalization of Goursat's problem is the Darboux-Picard problem: to find the solution of a hyperbolic equation, or a second-order hyperbolic system,

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