Heat Equation
∂u/∂t = α∇²u
Wave Equation
∂²u/∂t² = c²∇²u
Navier-Stokes
∂u/∂t + (u·∇)u = - (1/ρ)∇p + ν∇²u
Schrödinger
iℏ ∂ψ/∂t = Ĥψ
Burgers'
∂u/∂t + u ∂u/∂x = ν ∂²u/∂x²
KdV
∂u/∂t + 6u ∂u/∂x + ∂³u/∂x³ = 0
Diffusion-Reaction
∂u/∂t = D∇²u + f(u)
Black-Scholes
∂V/∂t + ½σ²S² ∂²V/∂S² + rS ∂V/∂S - rV = 0
Poisson
∇²ϕ = ρ/ε₀
Laplace
∇²ϕ = 0
Helmholtz
∇²u + k²u = 0
Fokker-Planck
∂P/∂t = -∇·(FP) + D∇²P
Allen-Cahn
∂u/∂t = ε²∇²u + u - u³
Ginzburg-Landau
∂A/∂t = A + (1+iβ)∇²A - (1+ic)|A|²A
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