A partial differential equation of second-order, i.e., one of the form A u_(x x) + 2B u_(x y) + C u_(y y) + D u_x + E u_y + F = 0, is called hyperbolic if the matrix Z congruent [A | B B | C] satisfies det(Z)<0. The wave equation is an example of a hyperbolic partial differential equation.

elliptic partial differential equation | parabolic partial differential equation | partial differential equation