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The 43 pages that link to Heat equation, each with the reason it gives.

• Fourier transformRelated: Fourier developed his decomposition methods to solve heat-flow problems.

• Fourier seriesRelated: Fourier series solve heat-flow problems by evolving each frequency component separately.

• Heat transferBroader topic: It models how conduction spreads temperature through a material.

• Boundary conditionsRelated: Its solutions depend on temperatures or heat fluxes prescribed at material boundaries.

• Differential equationBroader topic: It is a canonical model of change distributed through space.

• Partial differential equationBroader topic: Its smoothing evolution is the standard example of a parabolic PDE.

• Initial-value problemBroader topic: Its future temperature field is determined by an initial temperature distribution.

• Boundary value problemRelated: Spatial boundary conditions control heat entering or leaving the modeled region.

• Green's functionBroader topic: Its heat kernel gives the response to an instantaneous point injection.

• GradientRelated: Heat flux is proportional to the negative temperature gradient.

• Fourier analysisRelated: Fourier developed his series methods to solve problems of heat propagation.

• Wave equationCompared with: It smooths disturbances over time, unlike the wave equation's traveling fronts.

• Partial derivativeRelated: Its spatial and temporal derivatives encode how temperature changes.

• Laplace's equationCompared with: Its steady states reduce to Laplace's equation when internal sources are absent.

• Initial conditionRelated: Its time-dependent solutions use an initial temperature distribution.

• Thermal diffusivityRelated: Thermal diffusivity is the coefficient multiplying the spatial temperature-curvature term.

• LaplacianRelated: The Laplacian gives the spatial spreading term in the heat equation.

• Harmonic analysisRelated: Fourier used oscillatory series to solve this equation.

• Joseph FourierRelated: Fourier developed a mathematical account of heat diffusion using this equation.

• Finite volume methodRelated: Finite volume balances can discretize heat fluxes while preserving energy accounting.

• Dirichlet boundary conditionRelated: Fixed boundary temperatures model surfaces held at prescribed temperatures.

• Gaussian functionRelated: Its point-source solution is Gaussian, linking the curve to diffusion.

• Linear differential equationBroader topic: It is a central linear partial differential equation for diffusion.

• Potential theoryCompared with: It describes time-dependent smoothing, unlike the static harmonic fields central here.

• Vector calculusRelated: Its spatial diffusion term is the Laplacian of temperature.

• Diffusion equationBroader topic: It is the diffusion equation applied to temperature, with thermal diffusivity as its coefficient.

• Fourier's lawNarrower topic: Combining Fourier's law with energy conservation yields the conduction heat equation.

• Separation of variablesRelated: Separation produces spatial eigenfunctions whose coefficients decay exponentially in time.

• Dirichlet problemRelated: Prescribed wall temperatures give Dirichlet boundary data for heat diffusion.

• Spectral theoremRelated: Eigenfunction expansions express heat evolution through the spectrum of the spatial operator.

• Black–Scholes equationCompared with: A change of variables transforms the Black–Scholes equation into this diffusion equation.

• Ricci flowCompared with: Ricci flow resembles nonlinear heat diffusion, with curvature replacing a fixed scalar field.

• Sturm–Liouville theoryRelated: Separation of variables converts many heat problems into Sturm–Liouville eigenvalue problems.

• Feynman–Kac formulaRelated: Kac's probabilistic interpretation of its solutions was a precursor to the general formula.

• Theta functionRelated: Theta series give fundamental solutions and periodic heat kernels.

• Parabolic partial differential equationBroader topic: It is the canonical linear example of parabolic evolution.

• Flow (mathematics)Compared with: Its evolution smooths whole fields, whereas an ordinary vector-field flow transports individual points.

• Lax equivalence theoremBroader topic: Finite-difference approximations to this evolution equation are commonly analyzed using the theorem.

• Method of linesBroader topic: Spatial discretization yields diffusion ODE systems commonly advanced by this approach.

• Crank–Nicolson methodRelated: It is the standard diffusion equation used to illustrate the method’s properties.

• De Bruijn–Newman constantRelated: The function family can be expressed through backward heat flow, which drives zero motion.

• Diffusion and random walksRelated: Heat spreads mathematically like a diffusing quantity.

• Numerical methods for partial differential equationsBroader topic: It is a standard test case for time-dependent parabolic solvers.