Boundary value problems | Partial differential equations

Stefan problem

In mathematics and its applications, particularly to phase transitions in matter, a Stefan problem is a particular kind of boundary value problem for a system of partial differential equations (PDE), in which the boundary between the phases can move with time. The classical Stefan problem aims to describe the evolution of the boundary between two phases of a material undergoing a phase change, for example the melting of a solid, such as ice to water. This is accomplished by solving heat equations in both regions, subject to given boundary and initial conditions. At the interface between the phases (in the classical problem) the temperature is set to the phase change temperature. To close the mathematical system a further equation, the Stefan condition, is required. This is an energy balance which defines the position of the moving interface. Note that this evolving boundary is an unknown (hyper-)surface; hence, Stefan problems are examples of free boundary problems. Analogous problems occur, for example, in the study of porous media flow, mathematical finance and crystal growth from monomer solutions. (Wikipedia).

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B06 Example problem with separable variables

Solving a differential equation by separating the variables.

From playlist Differential Equations

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From playlist Differential Equations

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B04 Example problem with separable variables

Solving a differential equation by separating the variables.

From playlist Differential Equations

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B07 Example problem with separable variables

Solving a differential equation by separating the variables.

From playlist Differential Equations

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B25 Example problem solving for a Bernoulli equation

See how to solve a Bernoulli equation.

From playlist Differential Equations

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B05 Example problem with separable variables

Solving a differential equation by separating the variables.

From playlist Differential Equations

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From playlist Differential Equations

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From playlist The Yale Development Dialogues

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From playlist Probability and Statistics

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From playlist Seminar In the Analysis and Methods of PDE (SIAM PDE)

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From playlist Bernoulli Differential Equations

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From playlist Semantics in Linguistics

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From playlist Bernoulli Differential Equations

Related pages

Nondimensionalization | Surface (mathematics) | Phase transition | Dimension | Mathematics | Curve | Partial differential equation | Self-similar solution | Heat equation | Conservation of energy | Hypersurface | Boundary value problem | Neumann boundary condition | Free boundary problem | Well-posed problem | Cahn–Hilliard equation | Heat flux | Advection