Elliptical Equations #CFD #Steady #unsteady #Classifications #PDEs #Elliptic #Hyperbolic #Parabolic

Elliptic equations have no real characteristic curves, curves along which it is not possible to eliminate at least one second derivative of from the conditions of the Cauchy problem.[1] Since characteristic curves are the only curves along which solutions to partial differential equations with smooth parameters can have discontinuous derivatives, solutions to elliptic equations cannot have discontinuous derivatives anywhere. This means elliptic equations are well suited to describe equilibrium states, where any discontinuities have already been smoothed out.