gptkbp:instanceOf
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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
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gases
liquids
solids
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gptkbp:boundary_conditions
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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
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1822
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gptkbp:formedBy
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gptkb:Joseph_Fourier
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gptkbp:generalizes
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fractional heat equation
nonlinear heat equation
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gptkbp:governs
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distribution of heat in a region over time
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https://www.w3.org/2000/01/rdf-schema#label
|
heat equation
|
gptkbp:main_variable
|
gptkb:time_zone
gptkb:temperature
spatial coordinates
|
gptkbp:mathematical_form
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∂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
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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
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gptkbp:solution_property
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existence of solution
maximum principle
smoothing effect
uniqueness of solution
|
gptkbp:type
|
parabolic PDE
|
gptkbp:used_in
|
engineering
finance
thermodynamics
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gptkbp:bfsParent
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gptkb:Differential_equations
gptkb:Ricci_flow
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gptkbp:bfsLayer
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5
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