Advanced Analytic Self-Similar Solutions of Regular and Irregular Diffusion Equations

Imre Ferenc Barna () and Laszlo Matyas ()
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Imre Ferenc Barna: Wigner Research Centre for Physics, Konkoly–Thege Miklós út 29-33, H-1121 Budapest, Hungary

Mathematics, 2022, vol. 10, issue 18, 1-17

Abstract: We study the diffusion equation with an appropriate change of variables. This equation is, in general, a partial differential equation (PDE). With the self-similar and related Ansatz, we transform the PDE of diffusion to an ordinary differential equation. The solutions of the PDE belong to a family of functions which are presented for the case of infinite horizon. In the presentation, we accentuate the physically reasonable solutions. We also study time-dependent diffusion phenomena, where the spreading may vary in time. To describe the process, we consider time-dependent diffusion coefficients. The obtained analytic solutions all can be expressed with Kummer’s functions.

Keywords: partial differential equations; diffusion and thermal diffusion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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