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gptkbp:instanceOf
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gptkb:partial_differential_equations
|
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gptkbp:application
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gptkb:probability_theory
option pricing
image processing
population dynamics
|
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gptkbp:appliesTo
|
gases
liquids
solids
|
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gptkbp:boundary_conditions
|
gptkb:Dirichlet_condition
gptkb:Neumann_condition
Robin condition
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gptkbp:describes
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heat conduction
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gptkbp:field
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gptkb:mathematics
physics
|
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gptkbp:firstPublished
|
1822
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gptkbp:formedBy
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gptkb:Joseph_Fourier
|
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gptkbp:generalizes
|
fractional heat equation
nonlinear heat equation
|
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gptkbp:governs
|
distribution of heat in a region over time
|
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gptkbp:main_variable
|
gptkb:time_zone
gptkb:temperature
spatial coordinates
|
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gptkbp:mathematical_form
|
∂u/∂t = α∇²u
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gptkbp:method
|
gptkb:Green's_function
Fourier series
separation of variables
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gptkbp:parameter
|
thermal diffusivity
|
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gptkbp:relatedTo
|
gptkb:wave_equation
gptkb:Kolmogorov_forward_equation
gptkb:parabolic_partial_differential_equation
gptkb:Laplace_equation
gptkb:Fokker-Planck_equation
Brownian motion
calculus of variations
mathematical physics
numerical analysis
stochastic processes
diffusion equation
diffusion process
|
|
gptkbp:solution_property
|
existence of solution
maximum principle
smoothing effect
uniqueness of solution
|
|
gptkbp:type
|
parabolic PDE
|
|
gptkbp:used_in
|
engineering
finance
thermodynamics
|
|
gptkbp:bfsParent
|
gptkb:Laplace_operator
gptkb:Laplace–Beltrami_operator
gptkb:Burgers'_equation
gptkb:Perona–Malik_equation
gptkb:method_of_images_(mathematics)
|
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gptkbp:bfsLayer
|
6
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
heat equation
|