Partial differential equations

set of partial differential equations that describe how electric and magnetic fields are generated and altered by each other and by charges and currents

partial differential equation describing how the quantum state of a non-relativistic physical system changes with time

differential equation that contains unknown multivariable functions and their partial derivatives

relativistic quantum mechanical wave equation

system of nonlinear partial differential equations describing the motion of viscous fluids

numerical method for solving physical or engineering problems

equation constraining a quantity to flow only via adjacent locations; can express a locality principle

physical law that differentiable symmetries correspond to conservation laws

thumb|250px|Solitary wave (water waves)|Solitary wave in a laboratory [[wave channel]]

system of linear partial differential equations characterizing holomorphic (complex differentiable) functions

second-order partial differential equation whose solutions are the functions for which a given functional is stationary

partial differential equation of elliptic type with broad utility in mechanical engineering and theoretical physics

relativistic wave equation in quantum mechanics

special function over the surface of a sphere

equation of statistical mechanics

equation in classical mechanics

method

branch of mathematic studying harmonic functions

mathematical problem

describing pressure difference over an interface in fluid mechanics

equation that describes density changes of a material that is diffusing in a medium

functional relationship F between some input x and output y such that y=g(x) and g is Lipschitz in a neighbourhood of every x

problem of finding a function which solves a specified partial differential equation with prescribed boundary values

equation

concept in potential theory

theory of 2nd‐order linear ODEs that are eigenvalue equations of the operator 𝑤(𝑥)⁻¹((d∕d𝑥)𝑝(𝑥)d∕d𝑥+𝑞(𝑥))

property of certain dynamical systems

exactly solvable model of coupled oscillators

technique for solving hyperbolic partial differential equations

mathematical model for turbulence

class of second-order linear partial differential equations

class of problems in PDEs

connected open subset of a finite-dimensional vector space

describing the precessional motion of magnetization in a solid

operator on functions, defined by the composition of Fourier transformation, multiplication with a certain smooth function of both position and momentum, and inverse Fourier transformation

solutions of a certain class of inhomogeneous partial differential equations

local existence and uniqueness theorem for analytic partial differential equations associated with Cauchy initial value problems

quantum mechanical model of a quantum nonrelativistic particle subject to a classical spherically symmetric potential well

set of nonlinear differential equations used to approximate global atmospheric flow

theorem that a harmonic function’s maximum can only be at the boundary of its domain

a result in functional analysis with applications in the study of partial differential equations

green's function for Laplacian

Riesz potential defines an inverse for a power of the Laplace operator on Euclidean space.

set of partial differential equations that describe the flow below a pressure surface in a fluid

PDE named after statistician and biologist Ronald Fisher

mathematical method for integrodifferential equations

Partial differential operator

mathematical problem

relativistic wave equation describing the propagation of a free spin 1½ particle

set of equations with more equations than unknowns

branch of physics

mathematical solution

class of methods for solving partial differential equations

computer modeling of time-varying behavior of a dynamical system

half of the integral of the squared gradient of a function on its domain

method of solving system of linear algebrayes equations based on the use of a sequence of decreasing grids and operator

Physics theorem for symmetries of action

Equations of fluid dynamics