Boundary value problems | Partial differential equations
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).
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
B04 Example problem with separable variables
Solving a differential equation by separating the variables.
From playlist Differential Equations
B07 Example problem with separable variables
Solving a differential equation by separating the variables.
From playlist Differential Equations
B25 Example problem solving for a Bernoulli equation
See how to solve a Bernoulli equation.
From playlist Differential Equations
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 Seminar In the Analysis and Methods of PDE (SIAM PDE)
Ex: Solve a Bernoulli Differential Equation Using an Integrating Factor
This video explains how to solve a Bernoulli differential equation. http://mathispower4u.com
From playlist Bernoulli Differential Equations
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From playlist International Meeting 2022 AMS-EMS-SMF
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From playlist Bernoulli Differential Equations