Category:Partial differential equations

B

• [+] Boundary conditions (11 P)

D

• [+] Differential systems (5 P)
• [+] Domain decomposition methods (15 P)

E

• [+] Elliptic partial differential equations (1 C, 15 P)
• [+] Equations of fluid dynamics (60 P)

E cont.

• [+] Exactly solvable models (2 C, 39 P)

H

• [+] Hyperbolic partial differential equations (9 P)

I

• [+] Integrable systems (2 P)

P

• [+] Parabolic partial differential equations (9 P)
• [+] Potential theory (3 C, 24 P)

S

• [+] Sobolev spaces (16 P)
• [+] Solitons (23 P)

W

• [+] Wave mechanics (4 C, 74 P)

• List of partial differential equation topics

*

• Partial differential equation
• Consumption distribution
• Change of variables (PDE)

A

• Algebraic analysis
• Alternating direction implicit method
• Analytic semigroup

B

• Babuška–Lax–Milgram theorem
• Bateman transform
• Benjamin–Bona–Mahony equation
• Benjamin–Ono equation
• Bessel potential
• Bochner space
• Bogomol'nyi–Prasad–Sommerfield bound
• Borel's lemma
• Boundary value problem
• Burgers' equation

C

• Cahn–Hilliard equation
• Calabi flow
• Calogero-Degasperis-Fokas equation
• Camassa–Holm equation
• Cartan–Kähler theorem
• Cartan–Kuranishi prolongation theorem
• Cauchy momentum equation
• Cauchy problem
• Cauchy surface
• Cauchy–Kowalevski theorem
• Cauchy–Riemann equations
• Chaplygin's equation
• Clairaut's equation
• Computational electromagnetics
• Conserved current
• Constraint counting
• Continuity equation

D

• D'Alembert's formula
• D-module
• Davey–Stewartson equation
• Degasperis–Procesi equation
• Derivation of the Navier–Stokes equations
• Diffiety
• Diffuse element method
• Diffusion equation
• Dirac equation
• Dirichlet eigenvalue
• Dirichlet problem
• Dirichlet's energy
• Dirichlet's principle
• Discontinuous Galerkin method
• Dispersionless equation
• Dispersive partial differential equation
• Duhamel's principle
• Dynamic simulation

E

• Eikonal equation
• Einstein field equations
• Electromagnetic wave equation
• Elliptic boundary value problem
• Engineering treatment of the finite element method
• Ernst equation

E cont.

• Euler–Lagrange equation
• Euler–Poisson–Darboux equation
• Euler–Tricomi equation
• Exner equation
• Extended finite element method

F

• Finite element method
• First-order partial differential equation
• Fisher's equation
• Fourier integral operator
• Fundamental solution
• Föppl–von Kármán equations

G

• Gårding's inequality
• Generalized Korteweg-de Vries equation
• Generic scalar transport equation
• Green's function for the three-variable Laplace equation
• Groundwater flow equation

H

• Hadamard's method of descent
• Hamilton–Jacobi–Bellman equation
• Harmonic conjugate
• Hartree equation
• Hasegawa–Mima equation
• Hearing the shape of a drum
• Holmgren's uniqueness theorem
• Homogenization (mathematics)
• Homotopy principle
• Hunter–Saxton equation
• Hypoelliptic operator
• Hörmander's condition

I

• Inhomogeneous electromagnetic wave equation
• Integrability conditions for differential systems
• Integrable system
• Inverse scattering transform
• Ishimori equation
• Isothermal coordinates

J

• John's equation

K

• Kadomtsev–Petviashvili equation
• Kaup–Kupershmidt equation
• Klein–Gordon equation
• Korteweg–de Vries equation
• Kuramoto model

L

• Lamm equation
• Landau–Lifshitz model
• Large eddy simulation
• Larmor formula
• Lewy's example
• Lin-Tsien equation
• Lions–Lax–Milgram theorem
• List of nonlinear partial differential equations

M

• Madelung equations
• Mason-Weaver equation
• Maximum principle
• Maxwell's equations
• Maxwell's equations in curved spacetime
• Method of characteristics
• Method of lines
• Mixed boundary condition
• Monge equation
• Monge–Ampère equation

M cont.

• Multigrid method
• Multiple-point constraint

N

• Navier–Stokes equations
• Navier–Stokes existence and smoothness
• Newtonian potential
• Noether's second theorem
• Noether's theorem
• Nonlinear Schrödinger equation
• Numerical partial differential equations

O

• Obstacle problem
• Omega equation
• Overdetermined system

P

• Parametrix
• Particle in a spherically symmetric potential
• Perfectly matched layer
• Phase space method
• Poisson's equation
• Population balance equation
• Potential theory
• Primitive equations
• Pseudo-differential operator

R

• Rarita–Schwinger equation
• Relaxation method
• Ricci flow
• Richards equation
• Riemann–Hilbert problem
• Riesz potential

S

• Saint-Venant's compatibility condition
• Schrödinger equation
• Theoretical and experimental justification for the Schrödinger equation
• Screened Poisson equation
• Secondary calculus and cohomological physics
• Seiberg–Witten invariant
• Semi-elliptic operator
• Separation of variables
• Shallow water equations
• Signorini problem
• Solid harmonics
• Sommerfeld radiation condition
• Spectral element method
• Spherical harmonics
• Spherical mean
• Spheroidal wave function
• Stefan problem
• Stochastic processes and boundary value problems
• Streamline diffusion
• Swift-Hohenberg equation

V

• Variational inequality
• Vibrations of a circular drum
• Viscosity solution

W

• Wave
• Weak formulation
• Well-posed problem
• Weyl's lemma (Laplace equation)
• Wiener–Hopf method

Y

• Young–Laplace equation

Z

• Zakharov system
• Zakharov–Schulman system