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The 56 pages that link to Partial differential equation, each with the reason it gives.

• Fourier transformNarrower topic: Fourier transforms turn many constant-coefficient differential equations into algebraic equations in frequency.

• Finite element methodNarrower topic: Many finite element problems begin as partial differential equations over a spatial or spacetime domain.

• Schrödinger equationNarrower topic: Spatial versions of the Schrödinger equation are partial differential equations.

• Numerical analysisRelated: Discretization makes many spatially and temporally varying physical models solvable on computers.

• Differential equationBroader topic: It extends the concept to functions varying across several independent variables.

• Navier–Stokes equationsNarrower topic: Velocity and pressure vary across space and time, so their governing equations are partial differential equations.

• Ordinary differential equationCompared with: A PDE has multiple independent variables, unlike an ODE’s single independent variable.

• Continuity equationNarrower topic: The local continuity relation is a partial differential equation for density and velocity.

• Initial-value problemBroader topic: Evolution equations for spatially varying fields often pose initial data for a PDE.

• Bernhard RiemannRelated: Riemann studied how wave-like equations describe propagation and discontinuities.

• Heat equationNarrower topic: The heat equation is a canonical example of this broad equation class.

• Wave equationNarrower topic: The wave equation belongs to this broad class of equations.

• Poisson's equationNarrower topic: Poisson's equation belongs to this broad family of equations.

• Superposition principleNarrower topic: Many field and wave equations use superposition because they are linear partial differential equations.

• Laplace's equationNarrower topic: Laplace's equation is a central example of this broader equation class.

• Cellular automatonCompared with: Continuous field equations model spatial change without discrete cells and local state tables.

• Finite difference methodNarrower topic: Finite difference methods commonly replace these derivatives with grid-based formulas.

• Elliptic partial differential equationNarrower topic: Elliptic equations are one major class of partial differential equations.

• Nonlinear systemNarrower topic: Nonlinear partial differential equations model spatially extended systems.

• Functional analysisRelated: Functional analysis establishes existence and regularity of many PDE solutions.

• Cauchy problemNarrower topic: Many Cauchy problems concern partial differential equations with data on a surface.

• Harmonic functionNarrower topic: The Laplace equation places harmonic functions within the theory of differential equations.

• Harmonic analysisNarrower topic: Fourier methods convert many linear differential equations into simpler componentwise problems.

• Joseph FourierNarrower topic: The heat equation that motivated Fourier’s work belongs to this class.

• Finite volume methodNarrower topic: Finite volume schemes approximate partial differential equations, especially in conservation form.

• Reaction–diffusion systemNarrower topic: Reaction–diffusion dynamics are commonly expressed as coupled equations in space and time.

• Integral equationCompared with: Its local formulation often has an equivalent integral formulation using Green's functions.

• Jacques HadamardNarrower topic: Hadamard’s analysis of wave propagation and well-posedness centered on these equations.

• Linear differential equationBroader topic: Linearity also applies when derivatives are partial.

• Diffusion equationNarrower topic: The diffusion equation belongs to this broad class because it involves space and time derivatives.

• Separation of variablesNarrower topic: Separation of variables is principally a technique for solving this broader class of equations.

• Mathematical analysisRelated: Analysis supplies existence, regularity, and solution methods for equations governing physical systems.

• Ricci flowNarrower topic: Ricci flow is a nonlinear partial differential equation for a time-dependent metric.

• Terence TaoNarrower topic: Tao studies how solutions to important equations evolve, remain smooth, or form singularities.

• Wave mechanicsNarrower topic: The Schrödinger equation is a partial differential equation for a wavefunction.

• Fourier inversion theoremRelated: Fourier methods solve constant-coefficient equations by transforming and then inverting.

• Jean le Rond d’AlembertNarrower topic: His work on vibrating strings helped establish the study of these equations.

• Geometric analysisRelated: Many central geometric problems become equations for functions or geometric fields.

• Claude-Louis NavierNarrower topic: The equations associated with Navier describe fields that vary across space and time.

• Computational physicsRelated: Many physical laws are expressed as partial differential equations before discretization.

• Nonlinear Schrödinger equationNarrower topic: The nonlinear Schrödinger equation evolves a field across space and time using partial derivatives.

• Parabolic partial differential equationNarrower topic: Parabolic equations are one structural class of partial differential equations.

• Electromagnetic wave equationNarrower topic: The electromagnetic wave equation relates field derivatives across space and time.

• Multivariable calculusRelated: It is a principal application of multivariable differentiation.

• Cauchy–Kovalevskaya theoremNarrower topic: The theorem concerns local solutions to this broad class of equations.

• Method of linesNarrower topic: The method of lines begins with this class of equations and discretizes selected variables.

• Operator theoryRelated: Operator theory supplies tools for existence, uniqueness, and stability of solutions.

• Karen UhlenbeckRelated: Nonlinear partial differential equations provide the analytic tools central to her geometric work.

• Sofya KovalevskayaNarrower topic: Kovalevskaya’s theorem establishes local existence and uniqueness for a broad class of analytic equations of this kind.

• Cathleen Synge MorawetzNarrower topic: Morawetz built much of her career around existence, uniqueness, and behavior of solutions to these equations.