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Solutions for Multitime Reaction–Diffusion PDE

Author

Listed:
  • Cristian Ghiu

    (Department of Mathematical Methods and Models, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, RO-060042 Bucharest, Romania
    These authors contributed equally to this work.)

  • Constantin Udriste

    (Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, RO-060042 Bucharest, Romania
    Second address: Academy of Romanian Scientists, Ilfov 3, Sector 5, RO-050044 Bucharest, Romania.
    These authors contributed equally to this work.)

Abstract

A previous paper by our research group introduced the nonlinear multitime reaction–diffusion PDE (with oblique derivative) as a generalized version of the single-time model. This paper states and uses some hypotheses that allow the finding of some important explicit families of the exact solutions for multitime reaction–diffusion PDEs of any dimension that have a multitemporal directional derivative term. Some direct methods for determining the exact solutions of nonlinear PDEs from mathematical physics are presented. In the single-time case, our methods present many advantages in comparison with other known approaches. Particularly, we obtained classes of ODEs and classes of PDEs whose solutions generate solutions of the multitime reaction–diffusion PDE.

Suggested Citation

  • Cristian Ghiu & Constantin Udriste, 2022. "Solutions for Multitime Reaction–Diffusion PDE," Mathematics, MDPI, vol. 10(19), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3623-:d:932764
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    References listed on IDEAS

    as
    1. Matthew J Simpson, 2015. "Exact Solutions of Linear Reaction-Diffusion Processes on a Uniformly Growing Domain: Criteria for Successful Colonization," PLOS ONE, Public Library of Science, vol. 10(2), pages 1-11, February.
    2. Polyanin, Andrei D., 2019. "Functional separable solutions of nonlinear reaction–diffusion equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 282-292.
    3. Alexander V. Aksenov & Andrei D. Polyanin, 2021. "Methods for Constructing Complex Solutions of Nonlinear PDEs Using Simpler Solutions," Mathematics, MDPI, vol. 9(4), pages 1-31, February.
    Full references (including those not matched with items on IDEAS)

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