partial differential equation
61Frobenius theorem (differential topology) — In mathematics, Frobenius theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an overdetermined system of first order homogeneous linear partial differential equations. In modern geometric terms …
62Helmholtz equation — The Helmholtz equation, named for Hermann von Helmholtz, is the elliptic partial differential equation:( abla^2 + k^2) A = 0where abla^2 is the Laplacian, k is a constant, and the unknown function A=A(x, y, z) is defined on n dimensional… …
63Korteweg–de Vries equation — In mathematics, the Korteweg–de Vries equation (KdV equation for short) is a mathematical model of waves on shallow water surfaces. It is particularly notable as the prototypical example of an exactly solvable model, that is, a non linear partial …
64Groundwater flow equation — Used in hydrogeology, the groundwater flow equation is the mathematical relationship which is used to describe the flow of groundwater through an aquifer. The transient flow of groundwater is described by a form of the diffusion equation, similar …
65Dirac equation — Quantum field theory (Feynman diagram) …
66Omega equation — The omega equation is of great importance in meteorology and atmospheric physics. It is a partial differential equation for the vertical velocity, ω, which is defined as a Lagrangian rate of change of pressure with time, that is, . The equation… …
67Schrödinger equation — For a more general introduction to the topic, please see Introduction to quantum mechanics. Quantum mechanics …
68Diffusion equation — The diffusion equation is a partial differential equation which describes density fluctuations in a material undergoing diffusion. It is also used to describe processes exhibiting diffusive like behaviour, for instance the diffusion of alleles in …
69Monge–Ampère equation — In mathematics, a (real) Monge–Ampère equation is a nonlinear second order partial differential equation of special kind. A second order equation for the unknown function u of two variables x,y is of Monge–Ampère type if it is linear in the… …
70John's equation — is an ultrahyperbolic partial differential equation satisfied by the X ray transform of a function. It is named after Fritz John.Given a function f:mathbb{R}^n ightarrow mathbb{R} with compact support the X ray transform is the integral over all… …
