1.Many diffusion problems reach a stationary time-independent solution as t → ∞. The model problem from Sect. 9.2.4 is one example where u(x, t) = s(t) = const for t → ∞. When u does not depend on time, the diffusion equation reduces to −βu(x) = f (x), in one dimension, and −β∇2u = f (x), in 2D and 3D. This is the famous Poisson […]




