Partial differential equations Basic notions and classification Concept
Partial differential equation
Summary
A partial differential equation, or PDE, is an equation that relates an unknown function of several variables to its partial derivatives. It is the several-variable counterpart of an ordinary differential equation. PDEs describe heat flow, waves, fluids, electromagnetism, quantum mechanics and many other laws of physics, and they are central objects of geometry and probability. See the definition.
Where this leads
51 pages build on this one.
- Finite difference method
- Stefan problem
- Similarity solution
- Stochastic partial differential equation
- Schrödinger equation
- Dirac equation
- Hamilton–Jacobi equation
- Lewy's example
- Nonlinear Schrödinger equation
- Regularity theory
- Topology optimization
- Tricomi equation
- Global analysis
- Cauchy–Kovalevskaya theorem
- Ginzburg–Landau equation
- Euler equations
- Prolongation of a section to a jet bundle
- Linear PDE
- Quasilinear PDE
- Optimal control of partial differential equations
- Shallow water equations
- Lamé equations of elasticity
- Sine-Gordon equation
- Telegrapher's equations
- Spencer cohomology
- Obstacle problem
- Traveling wave
- Stefan problem as a variational inequality
- Navier–Stokes equations
- Complete integral
- Maxwell's equations
- Fully nonlinear PDE
- Boltzmann equation
- Korteweg–De Vries equation
- Biharmonic equation
- Integro-partial differential equation
- Transport equation
- Weak solution
- Lie group method for PDEs
- Helmholtz equation
- Shape optimization
- Dispersive partial differential equation
- Semilinear PDE
- Cartan–Kähler theorem
- Conservation law
- Vlasov equation
- Kadomtsev–Petviashvili equation
- Order of a PDE
- Free boundary problem
- A priori estimate
- Bäcklund transform
Further reading
About this page
| Tag | GC5BDZ6QBC |
|---|---|
| URI | m2://GC5BDZ6QBC |
| Kind | concept |
| Writing | W0 stub |
| MSC | 35A99 |
| Specializes | Differential equation |
| Same as |
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Special cases
- Navier–Stokes equations
- Parabolic partial differential equation
- Tricomi equation
- Fully nonlinear PDE
- Hamilton–Jacobi equation
- Ginzburg–Landau equation
- Mixed-type equation
- Quasilinear PDE
- Sine-Gordon equation
- Conservation law
- Hyperbolic partial differential equation
- Maxwell's equations
- Biharmonic equation
- Elliptic partial differential equation
- Gross–Pitaevskii equation
- Nonlinear Schrödinger equation
- Lamé equations of elasticity
- Korteweg–De Vries equation
- Boltzmann equation
- Helmholtz equation
- Kadomtsev–Petviashvili equation
- Transport equation
- Euler equations
- Vlasov equation
- Dirac equation
Used by
- Finite difference method
- Stefan problem
- Similarity solution
- Stochastic partial differential equation
- Schrödinger equation
- Dirac equation
- Hamilton–Jacobi equation
- Lewy's example
- Nonlinear Schrödinger equation
- Regularity theory
- Topology optimization
- Tricomi equation
- Global analysis
- Cauchy–Kovalevskaya theorem
- Ginzburg–Landau equation
- Euler equations
- Prolongation of a section to a jet bundle
- Linear PDE
- Quasilinear PDE
- Optimal control of partial differential equations
- Shallow water equations
- Lamé equations of elasticity
- Sine-Gordon equation
- Telegrapher's equations
- Spencer cohomology
- Traveling wave
- Navier–Stokes equations
- Complete integral
- Maxwell's equations
- Fully nonlinear PDE
- Boltzmann equation
- Korteweg–De Vries equation
- Biharmonic equation
- Integro-partial differential equation
- Transport equation
- Weak solution
- Lie group method for PDEs
- Helmholtz equation
- Shape optimization
- Dispersive partial differential equation
- Semilinear PDE
- Conservation law
- Vlasov equation
- Kadomtsev–Petviashvili equation
- Order of a PDE
- Free boundary problem
- A priori estimate
- Bäcklund transform