General form of the Euler-Poisson-Darboux equation and application of the transmutation method
| dc.contributor.author | Shishkina, Elina | |
| dc.contributor.author | Sitnik, Sergei | |
| dc.date.accessioned | 2022-06-08T14:12:14Z | |
| dc.date.available | 2022-06-08T14:12:14Z | |
| dc.date.issued | 2017-07-11 | |
| dc.description.abstract | In this article, we find solution representations in the compact integral form to the Cauchy problem for a general form of the Euler-Poisson-Darboux equation with Bessel operators via generalized translation and spherical mean operators for all values of the parameter k, including also not studying before exceptional odd negative values. We use a Hankel transform method to prove results in a unified way. Under additional conditions we prove that a distributional solution is a classical one too. A transmutation property for connected generalized spherical mean is proved and importance of applying transmutation methods for differential equations with Bessel operators is emphasized. The paper also contains a short historical introduction on differential equations with Bessel operators and a rather detailed reference list of monographs and papers on mathematical theory and applications of this class of differential equations. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 20 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Shishkina, E. L., & Sitnik, S. M. (2017). General form of the Euler-Poisson-Darboux equation and application of the transmutation method. Electronic Journal of Differential Equations, 2017(177), pp. 1-20. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15870 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Bessel operator | |
| dc.subject | Euler-Poisson-Darboux equation | |
| dc.subject | Hankel transform | |
| dc.subject | Transmutation operators | |
| dc.title | General form of the Euler-Poisson-Darboux equation and application of the transmutation method | |
| dc.type | Article |