Characteristics and Initial-Value Problems

Roughly speaking, characteristics are curves which carry information. They are particularly relevant in the study of “initial-value” problems ; that is, in solving partial differential equations, in which the solution surface is required to assume prescribed values “initially.” Such a problem presupposes the existence of a distinguished coordinate, ξ, where the equation ξ, = 0 defines the “initial ” surface. Of course, as we have seen in the last chapter, one needs some kind of compatibility between the equation and the initial surface. The notion of characteristic serves to classify and make more precise these intuitive ideas.