Well-posedness results for the wave equation generated by the Bessel operator
Бессель операторы арқылы туындаған толқын теңдеуi үшiн тұрақтылық нәтижелерi
Результаты корректности волнового уравнения, порожденного оператором Бесселя
Bekbolat B. Tokmagambetov N.
2021E.A.Buketov Karaganda State University Publish House
Bulletin of the Karaganda University. Mathematics Series
2021#101Issue 111 - 16 pp.
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].
Bessel operator , Hankel transform , inverse Hankel transform , Sobolev type space , wave equation
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Al-Farabi Kazakh National University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Belgium
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling
Department of Mathematics: Analysis
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