ABSTRACT
The two families of characteristic curves may be complex, real and repeated, or real and distinct, according to whether the discriminant, S2 - 4AC, is negative, zero, or positive, respectively. Accordingly, Eq. (111.21) is classified as follows:
Negative Zero Positive
Characteristic curves
Classification
Elliptic Parabolic Hyperbolic
Consequently, elliptic PDEs have no real characteristic paths, parabolic PDEs have one real repeated characteristic path, and hyperbolic PDEs have two real distinct characteristic paths.
