Classification of second-order PDEs

Summary

Linear second-order partial differential equations are sorted into elliptic, parabolic and hyperbolic equations. The type is given by the signs of the eigenvalues of the matrix of second-order coefficients. The three types behave very differently: elliptic equations describe equilibria, parabolic equations describe diffusion, and hyperbolic equations describe waves. The model cases are the Laplace equation, the heat equation and the wave equation. See the definition.