Stefan problem

E298871

free boundary problem mathematical problem partial differential equation model

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.

Try in SPARQL Jump to: Surface forms Disambiguation Statements Elicitation Referenced by

All labels observed (3)

Label	Occurrences
Stefan condition	2
Laplacian growth	1
Stefan problem canonical	1

How this entity was disambiguated

This entity first appeared as the object of triple T2789331 — 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: Stefan problem
Context triple: [Josef Stefan, knownFor, Stefan problem]

A. Smoluchowski coagulation equation
The Smoluchowski coagulation equation is a fundamental integro-differential equation in statistical physics that models how particles undergoing random collisions aggregate over time into larger clusters.
B. Cauchy problem
The Cauchy problem is a fundamental type of initial value problem in partial differential equations, where one seeks a solution satisfying prescribed data on a given initial surface.
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. Saffman–Taylor instability
The Saffman–Taylor instability is a fluid dynamics phenomenon in which a less viscous fluid penetrating a more viscous one in a confined geometry leads to finger-like interfacial patterns, often called viscous fingering.
E. Hilbert’s twenty-second problem
Hilbert’s twenty-second problem is one of David Hilbert’s famous list of 23 problems, concerning the uniformization of analytic relations and the representation of multi-valued analytic functions by single-valued ones on suitable Riemann surfaces.
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: Stefan problem
Target entity description: 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.

A. Smoluchowski coagulation equation
The Smoluchowski coagulation equation is a fundamental integro-differential equation in statistical physics that models how particles undergoing random collisions aggregate over time into larger clusters.
B. Cauchy problem
The Cauchy problem is a fundamental type of initial value problem in partial differential equations, where one seeks a solution satisfying prescribed data on a given initial surface.
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. Saffman–Taylor instability
The Saffman–Taylor instability is a fluid dynamics phenomenon in which a less viscous fluid penetrating a more viscous one in a confined geometry leads to finger-like interfacial patterns, often called viscous fingering.
E. Hilbert’s twenty-second problem
Hilbert’s twenty-second problem is one of David Hilbert’s famous list of 23 problems, concerning the uniformization of analytic relations and the representation of multi-valued analytic functions by single-valued ones on suitable Riemann surfaces.
F. None of above. chosen

Statements (49)

Predicate	Object
instanceOf	free boundary problem ⓘ mathematical problem ⓘ partial differential equation model ⓘ
application	casting processes ⓘ cryosurgery modeling ⓘ food freezing ⓘ glaciology ⓘ melting of ice ⓘ permafrost thawing ⓘ solidification of metals ⓘ
assumes	energy conservation at the moving interface ⓘ
boundaryType	free boundary ⓘ moving boundary ⓘ
canBe	one-phase Stefan problem ⓘ two-phase Stefan problem ⓘ
dependsOn	density ⓘ latent heat of phase change ⓘ specific heat ⓘ thermal conductivity ⓘ
describes	interface between solid and liquid phases ⓘ melting ⓘ motion of phase boundaries ⓘ phase-change processes ⓘ solidification ⓘ
field	applied mathematics ⓘ heat transfer ⓘ mathematical physics ⓘ
governingEquations	heat equation ⓘ
governs	speed of the phase-change front ⓘ
includesCondition	Stefan problem self-linksurface differs ⓘ surface form: Stefan condition
mathematicalNature	nonlinear problem ⓘ
namedAfter	Josef Stefan ⓘ
originCentury	19th century ⓘ
relatedConcept	Stefan problem self-linksurface differs ⓘ surface form: Stefan condition free boundary problem ⓘ heat equation ⓘ latent heat ⓘ
solutionMethod	front-tracking numerical methods ⓘ level-set methods ⓘ phase-field methods ⓘ similarity solutions ⓘ variational inequalities ⓘ
spatialDimension	multi-dimensional form ⓘ one-dimensional form ⓘ
timeDependent	true ⓘ
typicalInterface	interface between ice and water ⓘ
unknowns	moving boundary position ⓘ temperature field ⓘ
usedIn	mathematical modeling of phase transitions ⓘ

How these facts were elicited

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Josef Stefan → knownFor → Stefan problem ⓘ

Saffman–Taylor instability → relatedTo → Stefan problem ⓘ

this entity surface form: Laplacian growth

Stefan problem → includesCondition → Stefan problem self-linksurface differs ⓘ

this entity surface form: Stefan condition

Stefan problem → relatedConcept → Stefan problem self-linksurface differs ⓘ