Fractal and Fractional (Nov 2024)

The Diffusion Equation Involving the Dunkl–Laplacian Operator in a Punctured Domain

  • Bayan Bekbolat,
  • Gulzat Nalzhupbayeva,
  • Niyaz Tokmagambetov

DOI
https://doi.org/10.3390/fractalfract8120696
Journal volume & issue
Vol. 8, no. 12
p. 696

Abstract

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The purpose of this paper is to establish solvability results for both direct and inverse problems associated with the diffusion equation involving the Dunkl–Laplacian operator in a punctured domain. We demonstrate the existence and uniqueness of solutions for both types of problems. Additionally, explicit formulas for the solutions to the considered problems are derived.

Keywords