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Asenjo, F. A., & Hojman, S. A. (2021). Accelerating solutions to diffusion equation. Eur. Phys. J. Plus., 136(6), 677.
Abstract: We report accelerating diffusive solutions to the diffusion equation with a constant diffusion tensor. The maximum values of the diffusion density evolve in an accelerating fashion described by Airy functions. We show the diffusive accelerating behavior for one-dimensional systems, as well as for a general three-dimensional case. We also construct a modulated modified form of the diffusion solution that retains the accelerating features.