ABSTRACT
In Chapters 3 and 4 we considered PDEs that are first order in an initial value variable, which we term "time" just to facilitate the discussion. If these PDEs are also first order in the boundary value independent variables, they are generally termed first-order hyperbolic PDEs; the advection equation (3.55) is one example. If the PDEs are first order in the initial value variable and second order in the boundary value variables, they are termed parabolic; Fourier's second law, equation (4.99), is an example. We now consider PDEs which are: (1) second order in the initial value variable, and if they are also second order in the boundary value variables, they are termed secondorder hyperbolic, and (2) zeroth order in the initial value independent variable, i.e., the initial value variable does not appear in any partial derivatives, that are termed elliptic.
