Email this article POISSON FORMULA FOR SOLVING THE RADIAL CAUCHY PROBLEM FOR A SINGULAR ULTRAHYPERBOLIC EQUATION
- Authors: Lyakhov L.N1,2,3, Bulatov Y.N3
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Affiliations:
- Voronezh State University
- Lipetsk State Pedagogical University named after P.P. Semenov-Tyan-Shansky
- Yelets State University named after I.A. Bunin
- Issue: Vol 61, No 2 (2025)
- Pages: 229-241
- Section: PARTIAL DERIVATIVE EQUATIONS
- URL: https://ogarev-online.ru/0374-0641/article/view/299128
- DOI: https://doi.org/10.31857/S0374064125020086
- EDN: https://elibrary.ru/HWNDTA
- ID: 299128
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Abstract
The singular ultrahyperbolic equation (Δ𝐵𝛽)𝑦𝑢= (Δ𝐵𝛾)𝑥𝑢 is considered under the assumption that the I.A. Kipriyanov condition is satisfied, where fractional dimensions of the Δ𝐵𝛾 -operators included in the equation are equal to the same positive number 𝜎. Three types of solutions to the radial Cauchy problem are studied, one of them is based on the T-pseudoshift operator, generalized T-shift and S.A. Tersenov’s method for determining solutions to equations that degenerate on the boundary. Poisson formulas for solving the Cauchy problem for the Euler–Poisson–Darboux equation are given for various values of the parameters in this equation.
About the authors
L. N Lyakhov
Voronezh State University; Lipetsk State Pedagogical University named after P.P. Semenov-Tyan-Shansky; Yelets State University named after I.A. Bunin
Email: levnlya@mail.ru
Yu. N Bulatov
Yelets State University named after I.A. Bunin
Email: y.bulatov@bk.ru
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