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

Author

Listed:
  • Imre Ferenc Barna

    (Wigner Research Centre for Physics, Konkoly–Thege Miklós út 29-33, H-1121 Budapest, Hungary)

  • László Mátyás

    (Department of Bioengineering, Faculty of Economics, Socio-Human Sciences and Engineering, Sapientia Hungarian University of Transylvania, Libertătii sq. 1, 530104 Miercurea Ciuc, Romania)

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.

Suggested Citation

  • Imre Ferenc Barna & László Mátyás, 2022. "Advanced Analytic Self-Similar Solutions of Regular and Irregular Diffusion Equations," Mathematics, MDPI, vol. 10(18), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3281-:d:911323
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    References listed on IDEAS

    as
    1. Humam Kareem Jalghaf & Endre Kovács & János Majár & Ádám Nagy & Ali Habeeb Askar, 2021. "Explicit Stable Finite Difference Methods for Diffusion-Reaction Type Equations," Mathematics, MDPI, vol. 9(24), pages 1-21, December.
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