KnowraParabolic partial differential equationLinked fromLinked fromThe 5 pages that link to Parabolic partial differential equation, each with the reason it gives.All 5Broader topic 1Narrower topic 1Compared with 3Partial differential equationBroader topic: Parabolic equations spread disturbances while progressively smoothing their solutions.Elliptic partial differential equationCompared with: Parabolic equations evolve toward states that elliptic equations describe directly.Hyperbolic partial differential equationCompared with: The heat equation's instantaneous spreading contrasts with hyperbolic finite-speed propagation.Elliptic regularityCompared with: Parabolic smoothing arises through time evolution, unlike the spatial estimates of elliptic regularity.Feynman–Kac formulaNarrower topic: The classical formula applies to a class of linear equations of this type.