partial differential equation
C3712
concept
A partial differential equation is an equation that relates the partial derivatives of an unknown multivariable function, describing how it changes with respect to several independent variables.
All labels observed (17)
| Label | Occurrences |
|---|---|
| partial differential equation canonical | 20 |
| integro-differential equation | 3 |
| transport equation | 3 |
| elliptic partial differential equation | 2 |
| nonlinear Schrödinger equation | 2 |
| nonlinear partial differential equation | 2 |
| second-order differential equation | 2 |
| Kolmogorov equation | 1 |
| fluid dynamics equation | 1 |
| fourth-order partial differential equation | 1 |
| necessary condition for an extremum of a functional | 1 |
| nonlinear elliptic equation | 1 |
| parabolic partial differential equation | 1 |
| partial differential equation model | 1 |
| quasi-geostrophic equation | 1 |
| soliton equation | 1 |
| wave equation | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: partial differential equation
Generated description
A partial differential equation is an equation that relates the partial derivatives of an unknown multivariable function, describing how it changes with respect to several independent variables.
Instances (31)
| Instance | Via concept surface |
|---|---|
| Abreu equation | — |
| Klein–Gordon equation | — |
| Laplace equation | — |
| Schrödinger equation | — |
| Hamilton–Jacobi equation | — |
| Esaki–Tsu relation | transport equation |
|
Vlasov equation (for long-range interactions and negligible collisions)
surface form:
Vlasov equation
|
— |
| Cauchy–Euler equation | second-order differential equation |
| Kähler–Ricci flow | — |
| Stefan problem | partial differential equation model |
| Euler equations | fluid dynamics equation |
| Monge–Ampère equation | — |
| Korteweg–De Vries equation | nonlinear partial differential equation |
| Boltzmann–Kac equation | integro-differential equation |
|
Eugene P. Gross
surface form:
Gross–Pitaevskii equation
|
nonlinear Schrödinger equation |
| Nernst–Planck equation | transport equation |
| Boltzmann equation | integro-differential equation |
| Ricci flow | — |
| Kolmogorov backward equation | — |
| Smoluchowski coagulation equation | integro-differential equation |
| Charney equation | quasi-geostrophic equation |
| Euler–Lagrange equation | necessary condition for an extremum of a functional |
| Helmholtz equation | — |
|
Poisson
surface form:
Poisson equation
|
— |
| Poisson equation | — |
| Gross–Pitaevskii equation | nonlinear Schrödinger equation |
|
Cahn
surface form:
Cahn–Hilliard equation
|
— |
| Cahn–Hilliard equation | — |
| Bloch–Torrey equation | — |
| Plebański's heavenly equations | nonlinear partial differential equation |
| Fokker–Planck equation | — |