heat equation

GPTKB entity

Statements (51)
Predicate Object
gptkbp:instanceOf partial differential equations
gptkbp:application gptkb:probability_theory
option pricing
image processing
population dynamics
gptkbp:appliesTo gases
liquids
solids
gptkbp:boundary_conditions gptkb:Dirichlet_condition
gptkb:Neumann_condition
Robin condition
gptkbp:describes heat conduction
gptkbp:field gptkb:mathematics
physics
gptkbp:firstPublished 1822
gptkbp:formedBy gptkb:Joseph_Fourier
gptkbp:generalizes fractional heat equation
nonlinear heat equation
gptkbp:governs distribution of heat in a region over time
https://www.w3.org/2000/01/rdf-schema#label heat equation
gptkbp:main_variable gptkb:time_zone
gptkb:temperature
spatial coordinates
gptkbp:mathematical_form ∂u/∂t = α∇²u
gptkbp:method gptkb:Green's_function
Fourier series
separation of variables
gptkbp:parameter thermal diffusivity
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:Differential_equations
gptkb:Ricci_flow
gptkbp:bfsLayer 5