Nonlinear partial differential equation

Differential equations
Scope
Fields
Applied mathematics
Social sciences
List of named differential equations
Classification
Types
By variable type
Features
Relation to processes
Solution
Existence and uniqueness
General topics
Solution methods
People
List

In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different physical systems, ranging from gravitation to fluid dynamics, and have been used in mathematics to solve problems such as the Poincaré conjecture and the Calabi conjecture. They are difficult to study: almost no general techniques exist that work for all such equations, and usually each individual equation has to be studied as a separate problem.

The distinction between a linear and a nonlinear partial differential equation is usually made in terms of the properties of the operator that defines the PDE itself.[1]

  1. ^ Logan, J. David (1994). An Introduction to Nonlinear Partial Differential Equations. New York: John Wiley & Sons. pp. 8–11. ISBN 0-471-59916-6.