Eur. Phys. J. Plus (2021) 136: 677
https://doi.org/10.1140/epjp/s13360-021-01663-x

Regular Article

Accelerating solutions to diffusion equation

¹ Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, 7491169, Santiago, Chile
² Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ibáñez, 7491169, Santiago, Chile
³ Departamento de Física, Facultad de Ciencias, Universidad de Chile, 7800003, Santiago, Chile
⁴ Centro de Recursos Educativos Avanzados, CREA, 7500018, Santiago, Chile

^a felipe.asenjo@uai.cl

Received: 23 March 2021
Accepted: 11 June 2021
Published online: 21 June 2021

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.