On Structural Stability of Characteristic Nets and the Cauchy Problem for a Tricomi–Cibrario Type Equation

For a generic second-order linear partial differential equation on the plane, the problem of nonlocal normal forms and invariants of a family of its characteristics, as well as the current state of the corresponding theory, is discussed. Potential applications of this theory are demonstrated by the example of solving a special Cauchy problem for a mixed-type equation.