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- Duhamel's_principle abstract "In mathematics, and more specifically in partial differential equations, Duhamel's principle is a general method for obtaining solutions to inhomogeneous linear evolution equations like the heat equation, wave equation, and vibrating plate equation. It is named after Jean-Marie Duhamel who first applied the principle to the inhomogeneous heat equation that models, for instance, the distribution of heat in a thin plate which is heated from beneath. For linear evolution equations without spatial dependency, such as a harmonic oscillator, Duhamel's principle reduces to the method of variation of parameters technique for solving linear inhomogeneous ordinary differential equations.The philosophy underlying Duhamel's principle is that it is possible to go from solutions of the Cauchy problem (or initial value problem) to solutions of the inhomogeneous problem. Consider, for instance, the example of the heat equation modeling the distribution of heat energy u in Rn. The initial value problem iswhere g is the initial heat distribution. By contrast, the inhomogeneous problem for the heat equation iscorresponds to adding an external heat energy ƒ(x,t)dt at each point. Intuitively, one can think of the inhomogeneous problem as a set of homogeneous problems each starting afresh at a different time slice t = t0. By linearity, one can add up (integrate) the resulting solutions through time t0 and obtain the solution for the inhomogeneous problem. This is the essence of Duhamel's principle.".
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- Duhamel's_principle hasPhotoCollection Duhamel's_principle.
- Duhamel's_principle subject Category:Mathematical_principles.
- Duhamel's_principle subject Category:Partial_differential_equations.
- Duhamel's_principle subject Category:Wave_mechanics.
- Duhamel's_principle type Abstraction100002137.
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- Duhamel's_principle type DifferentialEquation106670521.
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- Duhamel's_principle type PartialDifferentialEquation106670866.
- Duhamel's_principle type PartialDifferentialEquations.
- Duhamel's_principle type Principle105913538.
- Duhamel's_principle type PsychologicalFeature100023100.
- Duhamel's_principle type Statement106722453.
- Duhamel's_principle comment "In mathematics, and more specifically in partial differential equations, Duhamel's principle is a general method for obtaining solutions to inhomogeneous linear evolution equations like the heat equation, wave equation, and vibrating plate equation. It is named after Jean-Marie Duhamel who first applied the principle to the inhomogeneous heat equation that models, for instance, the distribution of heat in a thin plate which is heated from beneath.".
- Duhamel's_principle label "Duhamel's principle".
- Duhamel's_principle label "Принцип Дюамеля".
- Duhamel's_principle label "デュアメルの原理".
- Duhamel's_principle label "杜哈梅原理".
- Duhamel's_principle sameAs デュアメルの原理.
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- Duhamel's_principle sameAs Q4378863.
- Duhamel's_principle sameAs Q4378863.
- Duhamel's_principle sameAs Duhamel's_principle.
- Duhamel's_principle wasDerivedFrom Duhamel's_principle?oldid=605966507.
- Duhamel's_principle isPrimaryTopicOf Duhamel's_principle.