Source: /cirosantilli/classification-of-second-order-partial-differential-equations-into-elliptic-parabolic-and-hyperbolic
= 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:
* https://math.stackexchange.com/questions/1090299/why-are-elliptic-parabolic-hyperbolic-pdes-called-elliptic-parabolic-hyperb