Consider the following second-order linear partial differential equation (PDE) in two variables:

Au_xx + Bu_xy + Cu_yy + Du_x + Eu_y + Fu = G(x,y)----(eqn 1)

Where A, B, C, D, E, F and G can be constants or functions of x and y.

The above PDE (eqn 1) is parabolic if B² - 4AC = 0. Parabolic PDE describe heat flow and diffusion processes.