ABSTRACT
A second-order semilinear partial differential equation in two independent variables has the form
a(x, y) ∂2w
∂x2 + 2b(x, y)
∂2w
∂x∂y + c(x, y)
∂2w
∂y2 = f
( x, y, w,
∂w
∂x , ∂w
∂y
) . (15.1.1.1)
This equation is classified according to the sign of the discriminant
δ = b2 – ac, (15.1.1.2)
where the arguments of the equation coefficients are omitted for brevity. Given a point (x, y), equation (15.1.1.1) is
parabolic if δ = 0, hyperbolic if δ > 0, elliptic if δ < 0.
