Post #4309947

dyou ever think it's kind of weird how partial differential equations are assigned one of three genders (elliptic, parabolic, hyperbolic) that in some cases follow a fixed rule (whether a discriminant is positive, zero, or negative for linear second order equations) but in other cases is completely arbitrarily proscribed based either on qualitative arguments ("it has wave-like solutions so it must be hyperbolic") or just going off of vibes?