Nonlinear partial differential equation information
Differential equations
Scope
Fields
Natural sciences
Engineering
Astronomy
Physics
Chemistry
Biology
Geology
Applied mathematics
Continuum mechanics
Chaos theory
Dynamical systems
Social sciences
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Population dynamics
List of named differential equations
Classification
Types
Ordinary
Partial
Differential-algebraic
Integro-differential
Fractional
Linear
Non-linear
By variable type
Dependent and independent variables
Autonomous
Coupled / Decoupled
Exact
Homogeneous / Nonhomogeneous
Features
Order
Operator
Notation
Relation to processes
Difference (discrete analogue)
Stochastic
Stochastic partial
Delay
Solution
Existence and uniqueness
Picard–Lindelöf theorem
Peano existence theorem
Carathéodory's existence theorem
Cauchy–Kowalevski theorem
General topics
Initial conditions
Boundary values
Dirichlet
Neumann
Robin
Cauchy problem
Wronskian
Phase portrait
Lyapunov / Asymptotic / Exponential stability
Rate of convergence
Series / Integral solutions
Numerical integration
Dirac delta function
Solution methods
Inspection
Method of characteristics
Euler
Exponential response formula
Finite difference (Crank–Nicolson)
Finite element
Infinite element
Finite volume
Galerkin
Petrov–Galerkin
Green's function
Integrating factor
Integral transforms
Perturbation theory
Runge–Kutta
Separation of variables
Undetermined coefficients
Variation of parameters
People
List
Isaac Newton
Gottfried Leibniz
Jacob Bernoulli
Leonhard Euler
Joseph-Louis Lagrange
Józef Maria Hoene-Wroński
Joseph Fourier
Augustin-Louis Cauchy
George Green
Carl David Tolmé Runge
Martin Kutta
Rudolf Lipschitz
Ernst Lindelöf
Émile Picard
Phyllis Nicolson
John Crank
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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]
^Logan, J. David (1994). An Introduction to Nonlinear Partial Differential Equations. New York: John Wiley & Sons. pp. 8–11. ISBN 0-471-59916-6.
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