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Partial Differential Eaquations - I

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List of partial differential equation topics
Partial differential equation
Consumption distribution
Change of variables (PDE)
Algebraic analysis
Alternating direction implicit method
Analytic semigroup
Babuška–Lax–Milgram theorem
Bateman transform
Benjamin–Bona–Mahony equation
Benjamin–Ono equation
Bessel potential
Black-oil equations
Bochner space
Bogomol'nyi–Prasad–Sommerfield bound
Borel's lemma
Boundary value problem
Burgers' equation
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'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
Domain (mathematical analysis)
Duhamel's principle
Dynamic simulation
Eikonal equation
Einstein field equations
Electromagnetic wave equation
Elliptic boundary value problem
Energy operator
Ernst equation
Euler–Lagrange equation
Euler–Poisson–Darboux equation
Euler–Tricomi equation
Exner equation
Extended finite element method
Finite element method
First-order partial differential equation
Fisher's equation
Föppl–von Kármán equations
Fourier integral operator
Fundamental solution
Gårding's inequality
Generalized Korteweg-de Vries equation
Generic scalar transport equation
Green's function for the three-variable Laplace equation
Groundwater flow equation
Hadamard's method of descent
Hamilton–Jacobi equation
Hamilton–Jacobi–Bellman equation
Harmonic conjugate
Hartree equation
Hasegawa–Mima equation
Hearing the shape of a drum
Hilbert's nineteenth problem
Holmgren's uniqueness theorem
Homogenization (mathematics)
Homotopy principle
Hörmander's condition
Hunter–Saxton equation
Hypoelliptic operator
Inhomogeneous electromagnetic wave equation
Integrability conditions for differential systems
Integrable system
Inverse scattering transform
Ishimori equation
Isothermal coordinates
John's equation
Kadomtsev–Petviashvili equation
Kaup–Kupershmidt equation
Klein–Gordon equation
Korteweg–de Vries equation
Kuramoto model
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
Madelung equations
Mason–Weaver equation
Maximum principle
Maxwell's equations
Maxwell's equations in curved spacetime
Method of characteristics
Method of lines
Method of quantum characteristics
Minkowski problem
Mixed boundary condition
Monge cone
Monge equation
Monge–Ampère equation
Motz's problem
Multidimensional systems
Multigrid method
Navier–Stokes equations
Navier–Stokes existence and smoothness
Newtonian potential
Noether's second theorem
Noether's theorem
Nonlinear Schrödinger equation
Numerical partial differential equations
Obstacle problem
Omega equation
Overdetermined system
Parametrix
Particle in a spherically symmetric potential
Perfectly matched layer
Perron method
Phase space method
Poisson's equation
Population balance equation
Potential theory
Primitive equations
Pseudo-differential operator
Pseudoanalytic function
Rarita–Schwinger equation
Relaxation method
Ricci flow
Richards equation
Riemann–Hilbert problem
Riesz potential
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 partial differential equation
Stochastic processes and boundary value problems
Streamline diffusion
Swift–Hohenberg equation
Underdetermined system
Variational inequality
Vibrations of a circular drum
Viscosity solution
Wave
Weak formulation
Well-posed problem
Weyl's lemma (Laplace equation)
Wiener–Hopf method
Yang–Mills–Higgs equations
Young–Laplace equation
Zakharov system
Zakharov–Schulman system