DOAJ Open Access 2021

Well-posedness results for the wave equation generated by the Bessel operator

B. Bekbolat N. Tokmagambetov

Abstrak

In this paper, we consider the non-homogeneous wave equation generated by the Bessel operator. We prove the existence and uniqueness of the solution of the non-homogeneous wave equation generated by the Bessel operator. The representation of the solution is given. We obtained a priori estimates in Sobolev type space. This problem was firstly considered in the work of M. Assal [1] in the setting of Bessel-Kingman hypergroups. The technique used in [1] is based on the convolution theorem and related estimates. Here, we use a different approach. We study the problem from the point of the Sobolev spaces. Namely, the conventional Hankel transform and Parseval formula are widely applied by taking into account that between the Hankel transformation and the Bessel differential operator there is a commutation formula [2].

Topik & Kata Kunci

Analysis Analytic mechanics Probabilities. Mathematical statistics

Penulis (2)

B. Bekbolat

N. Tokmagambetov

Format Sitasi

APA MLA BibTeX

Bekbolat, B., Tokmagambetov, N. (2021). Well-posedness results for the wave equation generated by the Bessel operator. https://doi.org/10.31489/2021m1/11-16

Akses Cepat

PDF tidak tersedia langsung

Cek di sumber asli →

Lihat di Sumber doi.org/10.31489/2021m1/11-16

Informasi Jurnal

Tahun Terbit: 2021
Sumber Database: DOAJ
DOI: 10.31489/2021m1/11-16
Akses: Open Access ✓