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gptkbp:instanceOf
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partial differential equations
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gptkbp:application
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gptkb:Probability_theory
Engineering
Finance
Thermal analysis
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gptkbp:borders
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gptkb:Dirichlet_boundary_condition
gptkb:Neumann_boundary_condition
Robin boundary condition
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gptkbp:canonicalForm
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∂u/∂t = α∇²u
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gptkbp:describes
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Heat conduction
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gptkbp:dimensions
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Two-dimensional
Three-dimensional
One-dimensional
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gptkbp:field
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gptkb:Mathematics
gptkb:Physics
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gptkbp:form
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∂u/∂t = α(∂²u/∂x² + ∂²u/∂y² + ∂²u/∂z²)
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gptkbp:formedBy
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gptkb:Joseph_Fourier
1822
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gptkbp:governs
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Temperature distribution in a given region over time
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gptkbp:hasSpecialCase
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gptkb:Laplace's_equation
gptkb:Steady-state_heat_equation
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https://www.w3.org/2000/01/rdf-schema#label
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Heat Equation
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gptkbp:mainVariable
|
Time
Temperature
Spatial coordinates
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gptkbp:parameter
|
Thermal diffusivity
|
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gptkbp:relatedConcept
|
gptkb:Kolmogorov_forward_equation
gptkb:Fokker-Planck_equation
Brownian motion
|
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gptkbp:relatedTo
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gptkb:Diffusion_Equation
gptkb:Laplace_Equation
gptkb:Wave_Equation
|
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gptkbp:solutionProperty
|
Satisfies energy dissipation
Satisfies maximum principle
Smooths initial data
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gptkbp:solvedBy
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gptkb:Green's_functions
Fourier series
Numerical methods
Separation of variables
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gptkbp:type
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Parabolic partial differential equation
|
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gptkbp:usedIn
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gptkb:Engineering_mathematics
gptkb:Environmental_science
Chemistry
Image processing
Biology
Stochastic processes
Geophysics
Mathematical physics
Material science
Option pricing
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gptkbp:bfsParent
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gptkb:Linear_Scale_Space
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gptkbp:bfsLayer
|
7
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