Dirichlet boundary conditions
E466250
Dirichlet boundary conditions are a fundamental type of boundary condition in differential equations and mathematical physics, specifying the values that a solution must take on the boundary of the domain.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Dirichlet boundary condition | 3 |
| Dirichlet boundary conditions canonical | 2 |
| Dirichlet boundary condition at finite distance | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4746240 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Dirichlet boundary conditions Context triple: [Peter Gustav Lejeune Dirichlet, notableWork, Dirichlet boundary conditions]
-
A.
Neumann boundary conditions in potential theory
Neumann boundary conditions in potential theory specify that the normal derivative of a potential function on a boundary is prescribed, modeling situations where flux across the boundary is controlled rather than the potential itself.
-
B.
Dirichlet conditions
Dirichlet conditions are a set of sufficient criteria on a function—such as piecewise continuity and having a finite number of extrema and discontinuities on an interval—that guarantee the convergence of its Fourier series representation.
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C.
Laplace equation
The Laplace equation is a fundamental second-order partial differential equation widely used in physics and engineering to describe steady-state phenomena such as electrostatics, gravitation, and heat conduction.
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D.
Sommerfeld radiation condition
The Sommerfeld radiation condition is a mathematical criterion in wave and scattering theory that selects physically meaningful, outward-radiating solutions to the Helmholtz equation at infinity.
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E.
Stefan problem
The Stefan problem is a classical mathematical model in heat transfer that describes how phase-change boundaries, such as the interface between ice and water, move over time.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Dirichlet boundary conditions Target entity description: Dirichlet boundary conditions are a fundamental type of boundary condition in differential equations and mathematical physics, specifying the values that a solution must take on the boundary of the domain.
-
A.
Neumann boundary conditions in potential theory
Neumann boundary conditions in potential theory specify that the normal derivative of a potential function on a boundary is prescribed, modeling situations where flux across the boundary is controlled rather than the potential itself.
-
B.
Dirichlet conditions
Dirichlet conditions are a set of sufficient criteria on a function—such as piecewise continuity and having a finite number of extrema and discontinuities on an interval—that guarantee the convergence of its Fourier series representation.
-
C.
Laplace equation
The Laplace equation is a fundamental second-order partial differential equation widely used in physics and engineering to describe steady-state phenomena such as electrostatics, gravitation, and heat conduction.
-
D.
Sommerfeld radiation condition
The Sommerfeld radiation condition is a mathematical criterion in wave and scattering theory that selects physically meaningful, outward-radiating solutions to the Helmholtz equation at infinity.
-
E.
Stefan problem
The Stefan problem is a classical mathematical model in heat transfer that describes how phase-change boundaries, such as the interface between ice and water, move over time.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
boundary condition
ⓘ
concept in partial differential equations ⓘ mathematical concept ⓘ |
| appliesTo |
elliptic partial differential equations
ⓘ
hyperbolic partial differential equations ⓘ parabolic partial differential equations ⓘ |
| assumes | boundary values are known a priori ⓘ |
| category | deterministic boundary conditions ⓘ |
| contrastedWith |
Neumann boundary conditions
NERFINISHED
ⓘ
Robin boundary conditions ⓘ |
| defines | values of a solution on the boundary of a domain ⓘ |
| domain | boundary of the spatial domain ⓘ |
| field |
applied mathematics
ⓘ
engineering ⓘ mathematical physics ⓘ numerical analysis ⓘ partial differential equations ⓘ |
| historicalPeriod | 19th century mathematics ⓘ |
| homogeneousForm | u(x)=0 on the boundary ⓘ |
| mathematicalForm | u(x)=g(x) for x on the boundary ⓘ |
| namedAfter | Johann Peter Gustav Lejeune Dirichlet NERFINISHED ⓘ |
| property |
can be non-homogeneous
ⓘ
can be space-dependent ⓘ can be time-dependent ⓘ |
| relatedConcept |
Dirichlet problem
NERFINISHED
ⓘ
boundary value problem ⓘ |
| role |
ensure uniqueness of solutions under suitable conditions
ⓘ
make boundary value problems well-posed ⓘ |
| specialCase | homogeneous Dirichlet boundary conditions ⓘ |
| specifies | solution values rather than derivatives ⓘ |
| usedFor |
modeling fixed displacement in elasticity
ⓘ
modeling fixed potential in electrostatics ⓘ modeling fixed temperature on a boundary ⓘ modeling prescribed concentration in diffusion problems ⓘ |
| usedIn |
Laplace equation
NERFINISHED
ⓘ
Poisson equation NERFINISHED ⓘ Schrödinger equation NERFINISHED ⓘ boundary element methods ⓘ electrostatics ⓘ finite difference methods ⓘ finite element methods ⓘ finite volume methods ⓘ fluid dynamics ⓘ heat equation ⓘ steady-state heat conduction ⓘ structural mechanics ⓘ wave equation ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Dirichlet boundary conditions Description of subject: Dirichlet boundary conditions are a fundamental type of boundary condition in differential equations and mathematical physics, specifying the values that a solution must take on the boundary of the domain.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Dirichlet boundary condition
this entity surface form:
Dirichlet boundary condition
this entity surface form:
Dirichlet boundary condition at finite distance
this entity surface form:
Dirichlet boundary condition