Classification of second order partial differential equations into elliptic, parabolic and hyperbolic

One major application of this classification is that different boundary conditions are suitable for different types of partial differential equations as explained at: which boundary conditions lead to existence and uniqueness of a second order PDE.

Bibliography:

www.cns.gatech.edu/~predrag/courses/PHYS-6124-12/StGoChap6.pdf 6.1 "Classification of PDE's" clarifies which boundary conditions are needed for existence and uniqueness of each type of second order of PDE: