User:Amatdiou/Books/Partial differential equations

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Partial differential equations[edit]

Category: Partial differential equations; List of partial differential equation topics; Change of variables (PDE); Consumption distribution; Partial differential equation; A priori estimate; Algebraic analysis; Alternating direction implicit method; User:JeffJohner/sandbox; Analytic semigroup; Asymptotic homogenization; Babuška–Lax–Milgram theorem; Bateman transform; Beltrami equation; Benjamin–Bona–Mahony equation; Benjamin–Ono equation; Bessel potential; Black-oil equations; Bochner space; Bogomol'nyi–Prasad–Sommerfield bound; Boltzmann equation; Borel's lemma; Boundary value problem; Burgers' equation; Allen–Cahn equation; Cahn–Hilliard equation; Calabi flow; Calogero–Degasperis–Fokas equation; Caloric polynomial; 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; Dirac equation in curved spacetime; 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; Elliptic partial differential equation; Energy operator; Ernst equation; Euler–Lagrange equation; Euler–Poisson–Darboux equation; Euler–Tricomi equation; Exner equation; Extended discrete element method; Extended finite element method; Finite element method; Dynamic Design Analysis Method; First-order partial differential equation; Fisher's equation; Föppl–von Kármán equations; Fourier integral operator; Free boundary problem; Fundamental solution; Gårding's inequality; Generalized Korteweg–de Vries 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; Homotopy analysis method; Homotopy perturbation method; Homotopy principle; Hopf lemma; Hörmander's condition; Hunter–Saxton equation; Hypoelliptic operator; Inhomogeneous electromagnetic wave equation; Integrability conditions for differential systems; Integrable system; Invariant factorization of LPDOs; Inverse scattering transform; Ishimori equation; Isothermal coordinates; John's equation; Kadomtsev–Petviashvili equation; Kansa method; Kaup–Kupershmidt equation; KdV hierarchy; Klein–Gordon equation; Korteweg–de Vries equation; Kuramoto model; Lamm equation; Landau–Lifshitz model; Landau–Lifshitz–Gilbert equation; Large eddy simulation; Larmor formula; Lewy's example; Lin–Tsien equation; Lions–Lax–Milgram theorem; Madelung equations; Mason–Weaver equation; Maximum principle; History of Maxwell's equations; List of textbooks in electromagnetism; Matrix representation of Maxwell's equations; 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; Neumann–Poincaré operator; Newtonian potential; Noether's second theorem; Noether's theorem; List of nonlinear partial differential equations; Nonlinear Schrödinger equation; Novikov–Veselov equation; Numerical partial differential equations; Obstacle problem; Omega equation; Overdetermined system; Parametrix; Partial differential algebraic equation; Particle in a spherically symmetric potential; Perfectly matched layer; Perron method; Petrov–Galerkin method; Phase space method; Poincaré–Lelong equation; Poisson's equation; Population balance equation; Potential theory; Primitive equations; Pseudo-differential operator; Pseudoanalytic function; Rarita–Schwinger equation; Reaction–diffusion–advection equation; Ricci flow; Richards equation; Riemann invariant; Riemann–Hilbert problem; Riesz potential; Saint-Venant's compatibility condition; 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; Sobolev spaces for planar domains; Solid harmonics; Solution algorithms for pressure-velocity coupling in steady flows; 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; Variational inequality; Vibrations of a circular membrane; Viscosity solution; Wave; Weak formulation; Well-posed problem; Weyl law; Weyl's lemma (Laplace equation); Whitham equation; Wiener–Hopf method; Yang–Mills–Higgs equations; Young–Laplace equation; Zakharov system; Zakharov–Schulman system
Category: Boundary conditions; Born–von Karman boundary condition; Cauchy boundary condition; Dirichlet boundary condition; Helical boundary conditions; Initial value problem; Neumann boundary condition; Perfect thermal contact; Periodic boundary conditions; Robin boundary condition
Category: Differential systems; Darboux's theorem; Differential ideal; Frobenius theorem (differential topology); Contact geometry; Contact (mathematics); Open book decomposition; Reeb vector field; Relative contact homology
Category: Elliptic partial differential equations; Elliptic operator; Agranovich–Dynin formula; Atiyah–Singer index theorem; Biharmonic Bézier surface; Biharmonic equation; Boggio's formula; Elliptic complex; Grad–Shafranov equation; Helmholtz equation; Hopf maximum principle; Infinity Laplacian; Laplace operator; Laplace's equation; P-Laplacian; PDE surface; Rayleigh–Faber–Krahn inequality; Schauder estimates; Signature operator
Category: Harmonic functions
Category: Harmonic functions; Harmonic function; Harmonic coordinates; Harnack's inequality; Harnack's principle; Hilbert transform; Kellogg's theorem; Kelvin transform; Pluriharmonic function; Poisson kernel; Schwarz reflection principle; Weakly harmonic function
Category: Hodge theory; Hodge theory; Dolbeault cohomology; Hodge conjecture; Hodge cycle; Hodge structure; Hodge–Tate module; Intermediate Jacobian; Malcev Lie algebra; Mumford–Tate group; P-adic Hodge theory; Period mapping; Ring of p-adic periods
Category: Equations of fluid dynamics; Advection; Barotropic vorticity equation; Basset–Boussinesq–Oseen equation; Batchelor vortex; Benedict–Webb–Rubin equation; Bernoulli's principle; Borda–Carnot equation; Boussinesq approximation (water waves); Buckley–Leverett equation; Darcy friction factor formulae; Darcy–Weisbach equation; Drag equation; Euler equations (fluid dynamics); Fanning friction factor; Faxén's law; Groundwater energy balance; Hadamard–Rybczynski equation; Hazen–Williams equation; Herschel–Bulkley fluid; Kármán–Howarth equation; Kaufmann (Scully) vortex; Kelvin's circulation theorem; Kozeny–Carman equation; Lamb–Oseen vortex; Mild-slope equation; Milne-Thomson circle theorem; Morison equation; Non-dimensionalization and scaling of the Navier–Stokes equations; Orr–Sommerfeld equation; Oseen equations; Pipe network analysis; Pressure-correction method; Prony equation; Rankine vortex; Rankine–Hugoniot conditions; Rayleigh–Plesset equation; Relativistic Euler equations; Reynolds transport theorem; Starling equation; Stokes flow; Stokes' paradox; Stream thrust averaging; Taylor–Goldstein equation; Velocity potential; Vorticity equation; Washburn's equation
Category: Exactly solvable models; List of integrable models; Arnold's cat map; Bäcklund transform; Baker's map; Bethe ansatz; Bullough–Dodd model; Chiral Potts curve; Corner transfer matrix; Domino tiling; Dym equation; Eight-vertex model; Gingerbreadman map; Hard hexagon model; Ice-type model; Ising model; Kramers–Wannier duality; Lax pair; Minimal models; Potts model; Quantum affine algebra; Quantum inverse scattering method; Schwinger model; Sine–Gordon equation; Spherical model; Square-lattice Ising model; Thirring model; Thirring–Wess model; Toda field theory; Toda lattice; Topological quantum number; Wess–Zumino–Witten model; Yang–Baxter equation; Yangian; Z N model
Category: Integrable systems; AKNS system; DBAR problem; Gelfand–Zeitlin integrable system; Nahm equations; Volterra lattice; W-algebra; Ward's conjecture
Category: Solitons; Topological defect; Robin Bullough; Compacton; Derrick's theorem; Dissipative soliton; Domain wall (string theory); Linear stability; Loop group; Non-topological soliton; Orbital stability; Oscillon; Peakon; Peregrine soliton; Nematicon; Soliton; Soliton (optics); Vakhitov–Kolokolov stability criterion
Category: Hyperbolic partial differential equations; Hyperbolic partial differential equation; D'Alembert operator; Petrovsky lacuna; Relativistic heat conduction; Riemann problem; Roe solver; Telegrapher's equations; Wave equation
Category: Parabolic partial differential equations; Parabolic partial differential equation; Autowave; Autowave reverberator; The Chemical Basis of Morphogenesis; Convection–diffusion equation; Feynman–Kac formula; Fokker–Planck equation; Heat equation; Heat kernel; Kolmogorov backward equations (diffusion); Mehler kernel; Reaction–diffusion system
Category: Potential theory; Axial multipole moments; Balayage; Capacity of a set; Cylindrical multipole moments; Double layer potential; An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism; Ewald summation; Extremal length; Focaloid; Harmonic measure; Laplace expansion (potential); Lebesgue spine; Multipole expansion; Pluripolar set; Potential energy surface; Quadrature domains; Riesz transform; Spherical multipole moments; Subharmonic function; Symmetrizable compact operator; Wolf summation
Category: Subharmonic functions; Fine topology (potential theory); Plurisubharmonic function; Polar set (potential theory)
Category: Sobolev spaces; Ehrling's lemma; Friedrichs' inequality; Gagliardo–Nirenberg interpolation inequality; Interpolation inequality; Interpolation space; Korn's inequality; Ladyzhenskaya's inequality; Lipschitz domain; Poincaré inequality; Rellich–Kondrachov theorem; Sobolev conjugate; Sobolev inequality; Sobolev space; Souček space; Szegő inequality; Trace operator; Trudinger's theorem
Category: Wave mechanics; Absolute phase; Acoustic phase conjugation; Acoustic wave; Airy beam; Amphidromic point; Amplitude; Bloch-Siegert shift; Clapotis; Coherence (physics); Coherence bandwidth; Coherent potential approximation; Dephasing; Diffraction formalism; Dispersion (water waves); Doppler effect; Double-slit experiment; Droplet-shaped wave; Electromagnetically induced grating; Electromagnetically induced transparency; Estimation of signal parameters via rotational invariance techniques; Faraday wave; Frequency; Fringe shift; Front velocity; Ground wave propagation; Group velocity; Hot chocolate effect; Huygens–Fresnel principle; Hydraulic jump; Hydraulic jumps in rectangular channels; Interference (wave propagation); Inverse Doppler effect; Lamb waves; Longitudinal mode; Longitudinal wave; Melde's experiment; Modal testing; Mutual coherence (physics); N-slit interferometric equation; Non-sinusoidal waveform; Nonlinear X-wave; Out Of Phase Stereo; Periodic travelling wave; Phase (waves); Phase angle; Phase change (waves); Phase conjugation; Phase inversion; Phase offset modulation; Phase response; Phase synchronization; Phase velocity; Photoacoustic Doppler effect; Plane wave; Quasiperiodicity; Rayleigh wave; Return loss; Rubens' tube; Rytov number; Scholte wave
Category: Diffraction; Diffraction