According to introductory texts on PDEs linear equations up to second order can be classified into three types:
- ellyptic
- parabolic
- hyperbolic
Obviously, this corresponds to the three types of conic sections. But what is the intuition of this classification? How are conic sections and PDEs related?
To clarify: I do understand why classification makes sense. But why do we specifically use these three terms (e.g ellyptic, parabolic, hyperbolic).
