Fundamental solution of the heat equation u_t = Δu on ℝⁿ: K(t,x) = (4πt)^{−n/2} exp(−|x|²/(4t)). Gaussian semigroup e^{tΔ}. Solves u_t = Δu with u(0, ·) = δ_0. Conserves total mass and satisfies the semigroup law K(t+s,·) = K(t,·) *…
Fundamental solution of the heat equation u_t = Δu on ℝⁿ: K(t,x) = (4πt)^{−n/2} exp(−|x|²/(4t)). Gaussian semigroup e^{tΔ}. Solves u_t = Δu with u(0, ·) = δ_0. Conserves total mass and satisfies the semigroup law K(t+s,·) = K(t,·) *…