Open AccessWell-posedness results for the wave equation generated by the Bessel operator
Author(s) -
Bayan Bekbolat,
Niyaz Tokmagambetov
Publication year - 2021
Publication title -
bulletin of the karaganda university-mathematics
Language(s) - English
Resource type - Journals
eISSN - 2663-5011
pISSN - 2518-7929
DOI - 10.31489/2021m1/11-16
Subject(s) - bessel function , mathematics , sobolev space , mathematical analysis , operator (biology) , bessel process , parseval's theorem , convolution (computer science) , wave equation , continuation , hankel transform , uniqueness , fourier transform , fourier analysis , classical orthogonal polynomials , biochemistry , chemistry , gegenbauer polynomials , repressor , orthogonal polynomials , gene , programming language , machine learning , artificial neural network , transcription factor , fractional fourier transform , computer science
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].