Work

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

Year: 2021

Type: article

Abstract: 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].

Source: BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS

DOI: 10.31489/2021m1/11-16

Authors: B. Bekbolat, N. Tokmagambetov

Institutions: Al-Farabi Kazakh National University, Ghent University, Institute of Mathematics and Mathematical Modeling

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Ministry of Education and Science of the Republic of Kazakhstan

OpenAlex ID: W3152258317

FWCI: 0.209

Cites: 13

Cited by: 1

Related to: 10