mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The...

In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different...

In mathematics, a hyperbolic partial differential equation of order n {\displaystyle n} is a partial differential equation (PDE) that, roughly speaking...

be defined as nonlinear, regardless of whether known linear functions appear in the equations. In particular, a differential equation is linear if it...

A parabolic partial differential equation is a type of partial differential equation (PDE). Parabolic PDEs are used to describe a wide variety of time-dependent...

In mathematics, an elliptic partial differential equation is a type of partial differential equation (PDE). In mathematical modeling, elliptic PDEs are...

of partial differential equation topics. Partial differential equation Nonlinear partial differential equation list of nonlinear partial differential equations...

In mathematics, the Korteweg–De Vries (KdV) equation is a partial differential equation (PDE) which serves as a mathematical model of waves on shallow...

Einstein tensor allows the EFE to be written as a set of nonlinear partial differential equations when used in this way. The solutions of the EFE are the...

See also Nonlinear partial differential equation, List of partial differential equation topics and List of nonlinear ordinary differential equations....

Burgers' equation or Bateman–Burgers equation is a fundamental partial differential equation and convection–diffusion equation occurring in various areas...

is a method that solves the initial value problem for a nonlinear partial differential equation using mathematical methods related to wave scattering.: 4960 ...

The Hamilton-Jacobi-Bellman (HJB) equation is a nonlinear partial differential equation that provides necessary and sufficient conditions for optimality...

the equation is not integrable, it allows for a collapse and wave turbulence. The nonlinear Schrödinger equation is a nonlinear partial differential equation...

The diffusion equation is a parabolic partial differential equation. In physics, it describes the macroscopic behavior of many micro-particles in Brownian...

ordinary differential equations List of nonlinear partial differential equations List of named differential equations List of stochastic differential equations...

mathematical physics, the Novikov–Veselov equation (or Veselov–Novikov equation) is a nonlinear partial differential equation. It is a two-dimensional analogue...

(real) Monge–Ampère equation is a nonlinear second-order partial differential equation of special kind. A second-order equation for the unknown function...

given data-set in the learning process, and can be described by partial differential equations (PDEs). Low data availability for some biological and engineering...

The sine-Gordon equation is a second-order nonlinear partial differential equation for a function φ {\displaystyle \varphi } dependent on two variables...

The Navier–Stokes equations (/nævˈjeɪ stoʊks/ nav-YAY STOHKS) are partial differential equations which describe the motion of viscous fluid substances...

proved the Nash embedding theorems by solving a system of nonlinear partial differential equations arising in Riemannian geometry. This work, also introducing...

Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the...

parabolic partial differential equation. The method is to reduce a partial differential equation (PDE) to a family of ordinary differential equations (ODEs)...

Liouville's equation in Euclidean space, see Liouville–Bratu–Gelfand equation. Liouville's equation, named after Joseph Liouville, is a nonlinear partial differential...

specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier...

and partial differential equations consist of distinguishing between linear and nonlinear differential equations, and between homogeneous differential equations...

In fluid dynamics, the general equation of heat transfer is a nonlinear partial differential equation describing specific entropy production in a Newtonian...

The Korteweg–de Vries–Burgers equation is a nonlinear partial differential equation: u t + α u x x x + u u x − β u x x = 0. {\displaystyle u_{t}+\alpha...

In mathematics, a dispersive partial differential equation or dispersive PDE is a partial differential equation that is dispersive. In this context, dispersion...